["Ratio, Proportion and\u00a0Variation 20.25 \t20.\t \u2009(i)\tFind the ratio of P : Q : R : S and proceed. \t\t(iii) M\u0007 arks scored by Bunny = \uf8eb 10 \uf8f6 (marks scored by Sunny). \uf8ec\uf8ed 7 \uf8f8\uf8f7 \t\t(ii)\tG\u0007 iven P : Q = Q : R = R : S = 1 : 2, find P : Q : R : S. 2\t 6.\t Divide both the numerator and the denominator \t\t(iii) R\u2019s share by y3. a 2 b 3 \t\t\t = term corresponding to R \u00d7 22, 515. \t27.\t Let the number be 10a + b. Given = . Sum of the terms of the ratio \t28.\t \u2009(i) Let the required number be x. \t21.\t \u2009\u2009\u2009(i) I\u0007 n b2 = ac, b is the mean proportion and c is the third proportional. \t\t(ii) 9\u2212x < 15 . 8+x 26 \t\t\u2009\u2009(ii) Let the two numbers be a and b. \t\t(iii) \u0007Solve the inequation to get least integer value \t\t(iii) (ab) = (24)2, b2 = 72a, solve for a and b. of x. \t22.\t Use the unitary method. \t29.\t \u2009\u2009\u2009\u2009(i) Frame the linear equation and solve it. \t23.\t \u2009\u2009\u2009(i) L\u0007 et the weights of the three pieces be x, 2x and \t\t(ii) \u0007Let the actual shares of Lava and Kusha be `5x 3x and their costs be C1, C2 and C3 respectively. and `7x respectively. \t\t\u2009\u2009(ii)=Cx31 (=2Cx2)3 C3 = 96, 336 . \t\t(iii) A\u0007 s the amount is (5x + 7x), one sixth of total (3x )3 (6x )3 amount = 2x. \t\t(iii) F\u0007 ind C1, C2 and C3 and then 96,336 \u2212 (C1 + \t\t(iv) T\u0007 he amount is divided in the ratio (5x + 2x) : C2 + C3). (7x - 2x). \t24.\t Let the weights of the three pieces be 2x, 3x and \t30.\t \u2009(i) \u0007Find the ratio of number of 1 rupee, 50 paise 5x and their costs be v1, v2 and v3 respectively. and 25 paise coins. \t\tv1 = 4x2k, v2 = 9x2k, v3 = 25x2k, \t\t(ii) \u0007The ratio of number of one rupee coins, num- \t\t96,000 = 100x2k ber of 50 paise coins and number 25 paise coins is (5 \u00d7 2) : (9 \u00d7 2) : (1 \u00d7 9), i.e., 10 : 18 : 9. \t\tx2k = 960 \t\t(iii) \u0007Let the number of one rupee coins, 50 paise coins Hints and Explanation \t\tv1 + v2 + v3 = 38x2k and 25 paise coins be 10x, 18x and 9x respectively. 1 1 \t\t= 38 \u00d7 960 = 36,480, \t\t(iv) Given (10x) + (18x ) 2 + (9x ) 4 = 425, \t\t\\\\ loss = 96,000 - 36,480 = 59,520. \uf8eb 18x \uf8f6 \uf8ec\uf8ed 2 \uf8f7\uf8f8 2\t 5.\t \u2009\u2009\u2009\u2009(i) F\u0007ind the ratio marks of Bunny, Sunny and \t\t\tFind , i.e., 9x. Bharat. \uf8eb 9\uf8f6 \uf8ec\uf8ed 8\uf8f8\uf8f7 \t\t\u2009\u2009(ii) \u0007Marks scored by sunny = (marks scored by Bharat). Level 2 \t32.\t Let the monthly incomes of Ram and Shyam be \t\t(ii)\t Given data can be expressed as x + 100y. 3x and 4x and their expenditures be 4y and 5y. x 300y 5 \t\t\t = 300 \u22c5 x + 400y = 6 . \t33.\t Let Anand\u2019s age k years ago, be 30 years. + 3\t 4.\t Let the number of students in A, B and C be 2x, \t\t(iii) \u0007Solve the above two equations and get the 3x and 4x. value of x. Sum of all the antecedents 3\t 9.\t Apply the concept of variation. Sum of all the consequents \t45.\t (i) Each ratio = . \t40.\t Let their present ages be 3x and 2x years. \t\t(ii) E\u0007 ach fraction is equal to the ratio of sum of the 4\t 3.\t (i) \u0007Let x be the fixed charge and y be the variable charge. numerators and the sum of the denominators of all the equivalent fractions.","20.26 Chapter 20 \t46.\t Name of the Ratio of Sugar and \t\t= 9(x \u2212 y) = 9 . Bakery Other Ingredients 10(x \u2212 y) 10 Mongunies 5 : 4 = 30 : 24 \t\tGiven that the expenditure of \u2009Mr Milind is `15,000. Karachi 13 : 12 = 26 : 24 \t\t \u2234 The expenditure of Mr Anand (in `) Bakers Inn 29 : 24 = 19=0 (15,000) 13, 500. \t\tFrom the above table, when the other ingredients are 24 units, their sugar quantities are 30 units, 4\t 9.\t The ratio of the present ages of Mr Dhuryodhana and Mr Dhushyasana is 5 : 4. 26 units and 29 units. \t\t \u2234 Mongunies biscuits are the sweetest. \t\tThe given ratio is the ratio of greater inequality. 4\t 7.\t Given that the ratio of shares of Mr Vaayu, Mr Jala \t\t \u2234 The ratio of their ages k years ago is greater than the ratio of their ages now. and Mr Agni is 3 : 4 : 7. \t\tShare of Mr Jala = `5600. \t\tBut 8 : 7 is less than 5 : 4. \t\t \u2234 The total sum (in `) = (3 + 4 + 7) 5\t 0.\t Let x +k = y \u21d2 x2 + kx = y2 + ky 4 y+k x \t\t(5600) = (14)(1400) = 19,600. \t\t\u21d2 k(x - y) = y2 \u2013 x2 \u21d2 k = \u2013(y + x). 4\t 8.\t Let the incomes of Mr Anand and Milind be 9x and 10x, and their savings be 9y and 10y. \t\t \u2234 The ratio of expenditures of Mr Anand and Mr Milind = 9x \u2212 9y 10x \u2212 10y Hints and Explanation Level 3 \t51.\t \u2009\u2009\u2009\u2009(i)\tNumber of boys be \u2018b\u2019 and number of girls be \t\t \tthe number of girls dressed in white = 4q \u2018g\u2019. \t\t \tthe number of boys dressed in blue = 5q. \t\t(ii)\tExpenses of each boy = g - 2 \t\t(iii)\tFrom the above data \t\t \texpenses of each girl = b - 2 \t\t \t 4 p + 4q = 12 , find \uf8eb p\uf8f6 from this equation. \t\t(iii) \u0007Solve b + g = 9 and the above equation and get 3 p + 5q 13 \uf8ec\uf8ed q \uf8f7\uf8f8 (g \u2212 2) in rupees. \t\t(iv)\tRequired ratio is (4p + 5q) : (3p + 4q), 5\t 3.\t (i)\tLet the number of students in the two classes A and B be 2x and 3x respectively. \t\t \ti.e., 4 \uf8eb p \uf8f6 + 5 : 3 \uf8eb p \uf8f6 + 4. \uf8ed\uf8ec q \uf8f7\uf8f8 \uf8ed\uf8ec q \uf8f7\uf8f8 \t\t(ii)\tGiven (3x \u2212 10) : (2x + 10) = 7 : 8. \t55.\t (i)\tLet the number of boys be \u2018b\u2019 and number of \t\t \tFind x from this equation. girls be \u2018g\u2019. \t\t(iii)\tLet y be the number of students to be shifted from A to B. \t\t(ii)\tExpenses of each boy = g + 1, \t\t(iv)\tSubstitute value of x in (2x - 10 + k) : (3x + \t\t \texpenses of each girl = b + 1. 10 - k) = 8 : 7 and find k. \t\t(iii)\tb( g + 1) = 7 . \t54.\t (i)\tFrame the linear equations and solve them. g(b) 6 \t\t(ii)\tGiven data can be expressed as \t\t(iv)\tSolve b + g = 11 and the above equation and \t\t \tthe number of boys dressed in white = 4p get (g + 1) in `. \t\t \tthe number of girls dressed in blue = 3p 5\t 6.\t Let the ages of Mrs. Anoukika and Mrs. Mythili be 5x years and 6x years. \t\tFrom the given data.","Ratio, Proportion and\u00a0Variation 20.27 \t\t5x + 6 = 6x \u21d2 x = 6 \t\tBy applying componendo\u2013dividendo theorem, \t\t\u2234 The sum of their present ages = 5x + 6x = 11x \t\taa22 + b2 = p2 + 11 . = 11(6) = 66 years. \u2212 b2 p2 \u2212 \t57.\t A B \t\tAs p is a constant, p2 + 1 is also a consonant. 4x 3x p2 \u2212 1 Income 5y 2y Expenditure 4x \u2013 5y 3x \u2013 2y \t\t\u2234 a2 + b2 and a2 - b2 vary directly. Savings 5\t 9.\t Let the required number of men be x. \t\tGiven, 3x \u2212 2y = 3000 \u21d2 x = 1000 + 2y 3 M1D1H1 M 2D2H2 \t\tNow, saving of A = 4x \u2212 5y = 4 \uf8ec\uf8eb\uf8ed1000 + 2y \uf8f6 \t\tWe have, W1 = W2 3 \uf8f8\uf8f7 \t\t\u22125y = 4000 + 8y \u2212 5y = 4000 \u2212 7y . \t\t(20)(115)(10) = (20 + x )(10)(12) 3 3 2 \t\t\u2234 The saving of A cannot be more than `4000. \t\t\u21d2 20 + x = 50 \u21d2 x = 30. \t\t\u2234 Hence, the correct answer is option(d). \t60.\t Let the amounts with Mr Umar and Mr Gumar be `3x and `4x respectively. 5\t 8.\t Given that a + b vary directly with a \u2013 b. \t\taa + b = k (constant ) \t\tGiven, 3x + 5 = 4 \u2212 b 4x \u2212 5 3 \t\tApplying componendo\u2013dividendo theorem, \t\t\u21d2 9x + 15 = 16x \u2013 20 \t\tba = k + 1 as k is constant, k +1 is also a constant. \t\t\u21d2 x = 5. Hints and Explanation k \u2212 1 k \u22121 \t\t\u2234 The amounts with Mr Umar and Mr Gumar are \t\t\u2234 a and b vary directly. `15 and `20 respectively. \t\tLet k +1 be p 15 \u2212 5 10 2 . k \u22121 20 + 5 25 5 \t\tThe required ratio = = = a a2 \t\t\u21d2 b = p \u21d2 b2 = p2. \t\tRatio of the amount with them is 2 : 5.","This page is intentionally left blank","1212CChhaapptteerr SKhinaermesataicnsd Dividends REMEMBER Before beginning this chapter, you should be able to: \u2022 Understand the terms related to banking \u2022 Outline ideas on financial market \u2022 Calculate the percentage values KEY IDEaS After completing this chapter, you should be able to: \u2022 Understand the terms such as shares and dividends \u2022 Know the nominal value of a share (NV) and market value of a share (MV) \u2022 Solve basic numerical problems on shares and dividends Figure 1.1","21.2 Chapter 21 INTRODUCTION The total amount of money required to start a business or a company is called \u2018capital\u2019. Generally, huge amounts of capital are required to start a company. It may be even hundreds of crores of rupees. It is not possible for a single person or two to arrange such large amount of money. So, the total amount of capital is divided into several small and equal units called \u2018shares\u2019. The management of the company invites investors to subscribe for these shares. Example: Suppose, the capital requirement of the company is `15 crores. The whole amount of capital can be divided into: 1.\t 15 lakh shares of `100 each, or 2.\t 30 lakh shares of `50 each, or 3.\t 60 lakh shares of `25 each. For every investment made, the management issues a share-certificate showing the value of each share and the number of shares held by each person. A person who purchases and owns the shares of a company is called \u2018a shareholder\u2019. Nominal Value of a Share (NV) Nominal value of a share is the value printed on the share certificate. It is also known as \u2018face value\u2019 (FV) or \u2018par value\u2019. Market Value of a Share (MV) Market value of a share is the value of the share at which it is bought or sold in the market. A share is said to be issued 1.\t at premium or above par, if MV > FV. 2.\t at discount or below par, if MV < FV. 3.\t at par, if MV = FV. Dividend Dividend is referred to as the annual profit distributed among the share holders. Dividend is always reckoned on the face value of a share. \u2002Notes\u2002 1.\t The face value of a share always remains the same. 2.\t The market value of a share changes from time to time. 3.\t Dividend is always paid on the face value of a share. 4.\t The number of shares held by a person \t = Total investment (or) Market value of each share \t = Total income (or) Income from each share \t = Total face value . Face value of each share","Shares and Dividends 21.3 Examples Based on Basic Concepts Example 21.1 Find the market value of a `300 share bought at a discount of `60. Solution Face value of the share = `300 The share is bought at a discount of `60. \\\\ Market value of the share = `(300 \u2212 60) = `240. Example 21.2 If a share of `150 is available at a premium of `50, then find the market value of 250 such shares. Solution Face value of the share = `150 The share is available at a premium of `50 Market value of each share = `(150 + 50) = `200 \\\\ Market value of 250 such shares = `(250 \u00d7 200) = `50,000. Example 21.3 Dhanik invests a certain amount in 300, `75 shares of a company paying 10% dividend. Find his annual income from this investment. Solution Face value of the share = `75 Number of shares bought = 300 Dividend paid = 10% Annual income from each share = `\uf8f0\uf8ef\uf8ee11000 (75)\uf8f9\uf8fb\uf8fa = `7.50. \u2234 Annual income from 300 shares = `(7.50 \u00d7 300) = `2250. Example 21.4 Ameer invests `24,200 in buying `100 shares of a company available at a premium of 10%. If the company pays a dividend of 15%, then find the number of shares bought by Ameer, and the rate of return on his investment. Solution Face value of each share = `100 The shares are available at a premium of 10%, i.e., 10% of 100 = `10. Market value of each share = `(100 + 10) = `110 Money invested = `24,200","21.4 Chapter 21 Number of shares bought = Total investment Market value of each share \t = 2=1412000 220 Dividend paid = 15% Annual income from each share = 15% of 100 = `15 \u21d2 Annual income from 220 shares = `(220 \u00d7 15) = `3300 The rate of return on his investment = Annual income \u00d7 100% Investment = 3300 \u00d7 100% 24200 \t 150 7 = 11 % = 13 11 % \u2234 Ameer gets a return of 13 7 % per annum on his investment. 11 Example 21.5 Which is better investment: `300 shares at `320 that pays a dividend of 10%, or `200 shares at `215 that pays a dividend of 10%? Solution Let the investment made in each case be `(320 \u00d7 215) Case 1:\u2002 `300 shares at `320 paying a dividend of 10% Annual income from each share = 10% of 300 = 10 \u00d7 100 = `30 100 Number of shares bought = Total investment = 320 \u00d7 215 = 215 Market value of each share 320 \u21d2 Annual income from 215 shares = `(215 \u00d7 30) = `6450. Case 2:\u2002 `200 shares at `215 paying a dividend of 10% 10 Annual income from each share = 10% of 200 = 100 \u00d7 200 = `20 Number of shares bought = Total investment = 320 \u00d7 215 = 320 Market value of each share 215 \u2234 Annual income from 320 shares = `(320 \u00d7 20) = `6400. So, it can be observed that the same amount of investment is made in each case, but the income is more in the first case. \u2234 10%, `300 shares at `320 is better investment. \u2002Note\u2002\u2002Sometimes, in case of start-up companies, the entire amount of authorized capital is not required. In such a situation a company may collect a part of the capital from the shares. It is collected equally from all share-holders. This amount is called, \u2018paid-up capital\u2019.","Shares and Dividends 21.5 When more money is required, the company has the right to collect the remaining amount from the share holders. The paid-up amount of the shares is the paid-up value of the shares. Example 21.6 The capital of a company is `250,000. If this capital is raised by issuing shares of `8 each, then how many shares are there? Solution =Number of shares F=Aacuethvoalruizeeodfcaapshitaarle 250, 000 = 31, 250. 8 Example 21.7 A company has 500 shares of `25 each. If `15 is paid-up for each share, then what is the paid- up capital? Also, find the amount to be paid in the second investment. Solution Paid-up amount per share = `15 Number of shares = 500 \u2234 Paid-up capital = `(500 \u00d7 15) = `7500 Total capital of the company = `(500 \u00d7 25) = `12,500 \u2234 Amount to be paid in the second instalment = `(12,500 \u2013 7500) = `5000. Example 21.8 The authorized capital of a company is `400,000, and the number of shares is 800. What is the face value of each share? If the paid-up capital is `260,000, then what is the paid-up value of each share? Solution Authorized capital = `400,000 Number of shares = 800 \u2234 Face value per share = ` 400, 000 = `500 800 Paid-up capital = `260,000 Number of shares = 800 \\\\ Paid-up amount per share = ` 260, 000 = `325. 800 Example 21.9 Which of the following is the least attractive scheme? (a) 5% of `120 shares at `150. (b) 6% `105 shares at `140. (c) 7% `90 shares at `125. (d) 8% `80 shares at `108.","21.6 Chapter 21 Solution Choice 1:\u2002 Face value\/share = `120 Dividend rate = 5% Annual income\/share = 5 (`120) = `6 100 Market value\/share = `150 Rate of return = 6 (100) = 4% 150 In a similar manner, the rates of return for the remaining choices can be worked out. Choice 2:\u2002 Annual income\/share = `6.30 Rate o=f return 16=4.30 (100) 9 %. 2 Choice 3:\u2002 Annual income\/share = `6.30 Rate of return = 6.3 (100) = 5.04%. 125 Choice 4:\u2002 Annual income\/share = `6.40 Rate o=f return 16=0.48 (100) 5 25 %. 27 The least attractive scheme is the scheme giving minimum rate of return. \\\\ Choice (a) gives the minimum rate of return among all the choices. Example 21.10 Mohan invested `24,000 in 8% `400 shares at `320. He sold them at `360 after one year. Find the total profit he earned. (in `) (a) 6540\t (b) 5400\t (c) 6600\t (d) 7200 Solution Face value\/share = `400 Dividend rate = 8% Annual income\/share = `32 Market value\/share = `320 Number of shares b=ought 2=43,20000 75 \\\\ Profit earned (in `) = 75(360 \u2013 320 + 32) = 5400. Example 21.11 Rahul bought 30 shares at `160 each. The par value of each share was `150. The dividend paid to him was at 6% per annum. By how much did his total investment exceed his total annual income? (in `). (a) 4530\t (b) 4430\t (c) 4630\t (d) 4330 Solution Face value\/share = `150","Shares and Dividends 21.7 Annual income\/share = 6% (`150) = `9 Total annual income = (30) (`9) = `270 Total investment = (30) (`160) = `4800 \\\\ The required value = `4800 \u2013 `270 = `4530. Example 21.12 Alex invested in the shares of a company. If the price of each share was `20 more, then his investment would be `6000 more. How many shares did he buy? (a) 300\t (b) 400\t (c) 360\t (d) 450 Solution Let us assume that Alex bought \u2018x\u2019 shares at a value of \u2018n\u2019. \u2234 The total investment on shares = `x \u22c5 n. The increased cost of a share = `x + 20. \u2234 From the given problem, (x + 20) \u00d7 n = xn + 6000 \u21d2 20n = 6000 \u21d2 n = 300. \u2234 Total number of shares = 300. Example 21.13 Imran invested equal amounts in the shares of two companies A and B. A offered him a 4% return while B offered him a 6% return. Which of the following can be the effective rate of return he receives on his entire investment? (a) 4%\t (b) 5%\t (c) 7%\t (d) 6% Solution The effective rate of return must lie between 4% and 6%. \u2234 Choice (b) can be the effective rate of return.","21.8 Chapter 21 TEST YOUR CONCEPTS Very Short Answer Type Questions \t1.\t A company has 5 lakh shares of `15 each. The face value is ______. capital of the company is ______. \t10.\t The person who subscribes in shares is called a \t2.\t If `150 share is quoted at a premium of `10, then ______. the market value of the share is `______. 1\t 1.\t Face value and market value of a share are `100 \t3.\t The annual income derived from each `200 share and `120 respectively, and the rate of return is at a premium of `30, paying 10% dividend is 10%. Then, dividend is ______ (in %). `______. 1\t 2.\t The paid-up capital of a company is `50,000. If the \t4.\t A man invests `13,200 in a company to buy `55 company has shares of face value of `25 in which shares. The number of shares he bought is _____. `20 is paid-up, then how many shares does it have? What is the authorized capital of the company? \t5.\t A company is selling shares at `120 each. Each has a par value of `100. The premium percentage is 1\t 3.\t A company has 500 shares of face value `50 in ______. which `30 is paid-up. The company collects `12,000 as the second instalment. What is the \t6.\t A company is selling shares at `96 each. Each has paid-up value of each share now? a par value of `120. The discount percentage is ______. \t14.\t The authorized capital of a company is `150,000 and the number of shares is 500. What is the face \t7.\t Mukesh invests `12,000 in a company to buy `100 value of each share? If the paid-up capital is `60,000, shares, paying 10% dividend. His annual income then what is the paid-up value of each share? from the shares is ______. 1\t 5.\t The authorized capital of a company is `50,000 \t8.\t Ratan had `2500 worth of shares. If he had 500 and the number of shares is 1000. If the paid-up shares, the face value of each share is ______. capital is `25,000, then the paid-up value of each share is `______. \t9.\t Pardhiv bought two types of shares A and B worth PRACTICE QUESTIONS `5000 each. If he bought 25 type A shares and 20 type B shares, then the difference between their Short Answer Type Questions \t16.\t When shares of face value `50 each are sold above (return) he gets on his money if the company pays par at `10 premium, then the money required to a dividend of 8% per annum. buy 30 such shares is ______. 1\t 9.\t Rakesh invested `27,000 in `27 shares of a com- \t17.\t A company has shares of face value `50 in which pany which pays a dividend of 10%. Find the `25 is paid-up and the paid-up capital is `10,000. market value of each share if he derives an annual Then, the authorized capital is ______. income of `540 from this investment, and also find the number of shares he bought. \t18.\t Ramesh bought 30 `200 shares of a company available at a premium of `25. Find the investment 2\t 0.\t A `100 share is bought at a premium of `25. If the made by Ramesh, and also the rate of interest investment is worth 9% per annum, then find the rate at which the company pays the dividend. Essay Type Questions \t21.\t Ranvir gets 8% per annum, on his investment \t22.\t Determine the amount that is to be invested in made in buying `80 shares of a company for `100 `200 shares available at a premium of `40, so each. What is the rate of dividend, and what is his that the annual income earned is `4800 from the annual dividend if he purchases 500 such shares? investment if the dividend offered is 12%.","Shares and Dividends 21.9 \t23.\t `33,000 is to be divided into two parts, such that 9.6% per annum. If the rate of dividend paid by the income from one part invested in `200 shares the company is 12%, then find the face value of at `250 for 10% dividend is the same as that from each share. the other investment which was invested in `120 shares at `150 for 12% dividend. Determine the \t25.\t If the investment made in buying 150 shares of a amounts invested in the two kinds of shares. company at `6 above par is `99,000, then find the face value of each share. \t24.\t An investment in buying 400 shares of a com- pany at a premium of `2.50 earns an income of CONCEPT APPLICATION Level 1 \t1.\t Amit bought 150 shares of `100 each. The paid- investment on each share, and the dividend from up value of each share is `60. Find the amount to each share. be paid as a second instalment. (in `) \t\t(a) 3 : 1\t\t (b) 4 : 1\t \t\t(a) 5000\t\t (b) 6000 \t\t(c) 5 : 1\t\t (d) 6 : 1 \t\t(c) 4500\t\t (d) 7500 \t7.\t Kalyan bought 600, `x shares at 20% premium from a company. If these had been bought at 20% \t2.\t Lavan had two types of shares. He had 800 shares discount, then his investment would have been of type A which gave him an annual dividend of `2400 less. How many `x shares have a total face `4000. If he had 200 more shares of type B than value of `20,000? A, which gave him the same annual dividend, then find his annual income from each share of B. (in `) \t\t(a) 2000\t\t (b) 1600 \t\t(a) 4\t\t (b) 3.50 \t\t(c) 1000\t\t (d) 800 \t\t(c) 2\t\t (d) 2.50 \t8.\t Aswin bought some shares of `75 from a com- pany. He paid `50 as a paid-up value of each share, \t3.\t Prakash had `120 shares of worth `7200. If he sold `32,000 as a paid-up capital. Find the total autho- PRACTICE QUESTIONS each of them for `30 more than its face value, then rized capital of Aswin. (in `) find his revenue from sales. (in `) \t\t(a) 7200\t\t (b) 8000 \t\t(a) 40,000\t\t (b) 48,000 \t\t(c) 9000\t\t (d) 6400 \t\t(c) 56,000\t\t (d) 60,000 \t4.\t Bhaskar bought `130 shares at a discount of `10. \t9.\t Shyam had some shares. He sold them at `12 dis- Find the number of shares he bought for `15,600. count. He realized `800 less than what he would have realized if he had sold them at `8 premium. \t\t(a) 120\t\t (b) 130 Find the number of shares he sold. \t\t(c) 140\t\t (d) 150 \t\t(a) 40\t\t (b) 50 \t5.\t Ashok bought `135 shares of a company at a pre- \t\t(c) 60\t\t (d) 80 mium. If the company provides the same premium amount as discount, then its market value will 1\t 0.\t Sashi bought `16 shares of a company at 25% divi- decrease by 50%. Find the premium. (in `) dend. Find the premium he paid for the shares (in `), if he received 20% rate of return. \t\t(a) 40\t\t (b) 45 \t\t(c) 50\t\t (d) 55 \t\t(a) 4\t\t (b) 3\t \t6.\t The total annual dividend obtained by Ajay \t\t(c) 6\t\t (d) 5 from the shares of a company was 25% of the total investment on them. Find the ratio of his 1\t 1.\t Kiran bought `10 shares of a company. He received a rate of return which was one-third of","21.10 Chapter 21 the dividend rate he received. Market value of \t\t(a) 6\t\t (b) 24\t each share is _____. (in `) \t\t(c) 32\t\t (d) 40 10 \t\t(a) 10\t\t (b) 3 \t \t14.\t Kishore invested a certain sum of money in two types of shares A and B of a company. The market value of \t\t(c) 30\t\t (d) 15 A is `30 more than that of B. He bought 400 shares of A and 300 shares of B. If he spent `18,000 more \t12.\t A company sells two types of shares A and B. on A than B, then find the market value of each The market value of A is 50% more than that of share of B. (in `) B and is 25% less than the face value of A. The market value of A and face value of B are equal. \t\t(a) 30\t\t (b) 40 By what percentage is the sum of the face values of both more than the sum of the market values \t\t(c) 50\t\t (d) 60 of both? \t15.\t Raju bought `40 shares of a company which had \t\t(a) 30%\t\t (b) 45%\t a market value of `60. He received a dividend of 30%. How much more (or) less would have been \t\t(c) 35%\t\t (d) 40% his annual dividend per share, if his dividend rate and rate of return were interchanged? \t13.\t Prasad invested `4000 to buy type A shares of a company. He invested in the same company to buy \t\t(a) `2 more per share. `4000 worth type B shares at face value. Market value of A equals face value of B. If he bought a \t\t(b) `3 more per share. total 64 shares of both, how many type A shares did he buy? \t\t(c) `4 less per share.\t \t\t(d) `6 less per share. Level 2 \t16.\t Gopal bought two types of shares P and Q, of a \t\t(a) 125\t\t (b) 100 company at their face values. The dividend rates provided by P and Q are 9% and 12%, respectively. \t\t(c) 120\t\t (d) 150 Gopal received an annual dividend of `4500 more PRACTICE QUESTIONS from P than from Q. Which of the following can \t19.\t If `4000 more was invested in share A, 20 more be the ratio of his investments in P and Q? shares can be purchased. If `4000 less was invested in A, 20 less shares can be purchased. Find the \t\t(a) 6 : 5\t\t (b) 5 : 4\t market value of A. (in `) \t\t(c) 4 : 3\t\t (d) 2 : 1 \t\t(a) 100\t\t (b) 150\t 1\t 7.\t If the rate of return and dividend from a share \t\t(c) 200\t\t (d) 300 are r\u2009% and d\u2009% respectively, find the premium\/ discount %, given d > r. 2\t 0.\t If the price of share A was `10 more, 50 less shares can be purchased by investing `x. If the price of \t\t(a) (r \u2212 d) % premium A was `20 less, 25 more shares can be purchased r by investing `x. Find the ratio of the price of each share and the number of shares purchased. (r \u2212 d ) % discount \t\t(b) d \t\t(a) 3 : 5\t\t (b) 5 : 3\t \t\t(c) (d \u2212 r ) % premium \t\t(c) 2 : 5\t\t (d) 5 : 2 r \t21.\t Which of the following can be concluded from the \t\t(d) (d \u2212 r ) % discount information given below? d \t\t\u2018Ajay bought, 12% `100 shares at `120\u2019. 1\t 8.\t If the rate of return from share P was 4% more, then the annual income from it would be `5 more. \t\t(a) Dividend per share = `12 Find its market value. (in `) \t\t(b) Rate of return = 10%","Shares and Dividends 21.11 \t\t(c) Both (a) and (b)\t 2\t 4.\t Which of the following is the least attractive scheme? \t\t(d) Neither (a) nor (b) 2\t 2.\t Hari invested `24,000 in buying shares worth `300 \t\t(a) 4% `40 shares at `50. each. The dividend paid to him was `20 per share. Find his total annual income from the shares. (in `) \t\t(b) 5% `50 shares at `60. \t\t(a) 1200\t\t (b) 2000 \t\t(c) 6% `60 shares at `70. \t\t(c) 2400\t\t (d) 1600 \t\t(d) 7% `70 shares at `80. 2\t 3.\t Shares worth `300 each were bought at a discount 2\t 5.\t Shares worth `200 each were bought at a premium of `60. The dividend paid was 6% per annum. of `40. The dividend paid was 8% per annum. Find the rate of return. Find the annual income per share. (in `) \t\t(a) 5% per annum\t (b) 6% per annum \t\t(a) 16\t\t (b) 12.6\t \t\t(c) 7.5% per annum\t (d) 8% per annum \t\t(c) 8\t\t (d) 19.2 Level 3 \t26.\t Rohit invested in two types of shares, P and Q, of \t\t(a) 600\t\t (b) 750\t a company. He purchased P at x% discount and Q \t\t(c) 800\t\t (d) 1000 at x% premium. If the total market value of each 3\t 0.\t Ashok invested in three types of shares, P, Q and R, of a company. He invested `5000 and `7500 in is equal, find the rate of effective discount (in per P and Q, respectively. He obtained rates of returns of 10%, 8% and 15% from P, Q and R, respectively. cent). (b) x2 % His annual income from the three types was a \t\t(a) 0.1%\t\t 400 total of `1550. How much did he invest in R? (in `) \t\t(c) x2 % \t\t (d) x2 % 200 100 2\t 7.\t Shares A and B have face values of `100 each. A is \t\t(a) 2500\t\t (b) 2000 sold at `x premium, and B is sold at `x discount. The rate of return from each is x%. The sum of the \t\t(c) 3500\t\t (d) 3000 PRACTICE QUESTIONS annual dividends from both is `10. Find x. 3\t 1.\t If Lokesh\u2019s investment was `4800 more, his annual \t\t(a) 4\t\t (b) 8 income would be `240 more. Find the rate of return. \t\t(c) 5\t\t (d) 10 \t\t(a) 4.5%\t\t (b) 4% \t28.\t Mahendar invested in three types of shares, P, Q and R, of a company. The total annual dividend \t\t(c) 5.5%\t\t (d) 5% he received from them was `1000. His investments in P, Q and R were `1000, `1000 and `3000, \t32.\t In the previous question, the rate of return is respectively. The rate of return he received from R was the average of the rates of return of the other \t\t(a) equal to the rate of dividend.\t two. Find the rate of return he received from R. \t\t(b) greater than the rate of dividend. \t\t(a) 10%\t\t (b) 20%\t \t\t(c) less than the rate of dividend. \t\t(c) 15%\t\t (d) 25% \t\t(d) Either (a) or (b) 2\t 9.\t Goutham invested `4000 to buy `125 shares of \t33.\t Kiran invests in the shares of a company. If he buys type A from a company and invested `4800 to buy 48 shares more, he will invest `1200 more. If he `120 shares of type B from it. He obtains 8% divi- buys 40 shares less, the total face value of his shares dend from A and 10% dividend from B. Find the will be `800 less. He must buy each share ______. total annual dividend he carried if the market value of each share equals its face value. (in `) \t\t(a) at par\t\t (b) below par \t\t(c) above par\t (d) Cannot be determined","21.12 Chapter 21 \t34.\t Rohit invested `39,600 in buying shares of nomi- \t35.\t In the previous question, if Rohit bought all shares at par, then find the rate at which the dividend was nal value of `100 at a 20% premium. The dividend paid to him. paid to him was at 6% per annum. Find his annual income. (in `) \t\t(a) 4.5%\t\t (b) 4% \t\t(a) 1950\t\t (b) 1980 \t\t(c) 5.5%\t\t (d) 5% \t\t(c) 1920\t\t (d) 2010 PRACTICE QUESTIONS","Shares and Dividends 21.13 TEST YOUR CONCEPTS \t9.\t `50 \t10.\t shareholder Very Short Answer Type Questions \t11.\t 12% 1\t 2.\t `62,500 \t1.\t `7,500,000 1\t 3.\t `54 \t2.\t `160 \t14.\t `120 \t3.\t `20 1\t 5.\t 25 \t4.\t 240 \t5.\t 20% \t19.\t `135; 200 \t6.\t 20% 2\t 0.\t 11.25% \t7.\t `1200 \t 8.\t 5 2\t 4.\t `10 \t25.\t `654 Short Answer Type Questions \t16.\t `1800 \t17.\t `20,000 1\t 8.\t `6750; 7.11% Essay Type Questions \t21.\t 10%; `4000 2\t 2.\t `48,000 2\t 3.\t `18,000; `15,000 CONCEPT APPLICATION 5. (b) \t 6. (b)\t 7. (a) \t 8. (b)\t 9. (a) \t 10. (a) ANSWER KEYS 15. (c) Level 1 \t1. (b)\t 2. (a)\t 3. (c) \t 4. (b)\t \t11. (c) \t 12. (d)\t 13. (c) \t 14. (d)\t Level 2 18. (a)\t 19. (c) \t 20. (c)\t 21. (c) \t 22. (d)\t 23. (c) \t 24. (a)\t 25. (a) \t16. (d)\t 17. (c) \t Level 3 28. (b)\t 29. (c)\t 30. (d)\t 31. (d) \t 32. (c)\t 33. (c) \t 34. (b)\t 35. (d) \t26. (d)\t 27. (c)","21.14 Chapter 21 CONCEPT APPLICATION Level 1 \t1.\t Find the paid-up capital. 1\t 0.\t (i)\tFind the annual dividend from each share. \t2.\t (i)\tAnnual dividend from each share \t\t(ii)\tFirst of all, find the market value of each share. = Total annual dividend . \t\t(iii)\tUse, FV \u00d7 Rate of dividend (RO) = MV \u00d7 Total number of shares Rate of return (RR). \t\t(ii)\tNumber of shares of type B = (Number of \t\t(v)\tPremium = MV \u2212 FV. shares of type A) + 1200. 1\t 1.\t (i)\tRate of dividend \u00d7 Face value = Rate of return \t\t(iii)\tTotal dividend on shares of type B = Total \u00d7 Market value. dividend on shares of type A = `4000. \t\t(ii)\tLet the rate of dividend be x%. \t\t(iv)\tAnnual income from each share of type \t\t(iii)\tNow, find the rate of return in terms of x. B = Total dividend for type B . Number of shares of type B \t\t(iv)\tThen, find the MV by using the formula, FV \u00d7 RD = MV \u00d7 RR. \t3.\t Find the number of shares. 1\t 2.\t (i)\tFind the face values of A and B. \t4.\t Find the market value of each share. \t\t(ii)\tLet the MV of each share of type B be `x. \t5.\t Let premium be `x. Find the market value of a share. \t\t(iii)\tNow, MV of each share of type A be 150% of x. \t6.\t Investment on each share = Total investment \t\t(iv)\tFV of each share of type B = MV of each share Dividend from each share Total dividend of type A. Hints and Explanation \t7.\t Find the market of a share in each case. \t\t(v)\tSimilarly find FV of each share of type A. \t8.\t (i)\tNumber of shares \t14.\t Difference of the investments is `18,000. 1\t 5.\t (i)\tFind the dividend from each share and rate of = Paid-up capital share . Paid-up value of each return. \t\t(ii)\tFirst of all, find rate of return by using the fol- \t\t(ii)\tNumber of shares = Total paid-up value . Paid-up value per share lowing formula: FV \u00d7 Rate of dividend = MV \u00d7 Rate of return. \t\t(iii)\tTotal capital = (Number of shares) (`75). \t\t(iii)\tLet x be the rate of return. Now, find 30% of 40 \u2212 x% of 40. \t9.\t Change in the price of a share is `20. Level 2 \t16.\t (i)\tThe ratio of rate of dividends on P and Q is \t\t(ii)\tAs d > r, shares are brought at premium. 3 : 4. \t\t(iii)\tLet the income from each share be \t\t(ii)\tIf the ratio of investments on P and Q is 4 : 3, dividend is same on both P and Q. d = i \u00d7 100 and r = i \u00d7 100. FV MV \t\t(iii)\tTherefore, required investment must be more \t\t(iii)\tPremium = MV \u2212 FV. Percentage of premium than 4 : 3 for the given condition. \t\t(iv)\tCheck the options to get the ratio which is = MV \u2212 FV \u00d7 100. more than 4 : 3. FV \t17.\t (i)\tAnnual dividend = d \u00d7 share value = r \u00d7 \t18.\t (i)\tRate of dividend \u00d7 Face value = Rate of return market value. 100 100 \u00d7 Market value.","Shares and Dividends 21.15 \t\t(ii)\tLet the market value be x and rate of return \t\tLet the rate of return be r\u2009%. be y. =\t\tr 21=480 (100) 7.5%. \t\t(iii)\tx(y + 4)% \u2212 xy% = 5. \t19.\t Obtain the relation between the amount invested \t24.\t Rate of return = Face value \u00d7 Rate of dividend and the number of shares. Market value 2\t 0.\t His investment in each case is same, i.e., `x. \t\tChoice (a): Rate of return = 40 \u00d7 4% 50 \t21.\t From the given information, dividend rate = 12%, face value\/share = `100 and market value\/share = \t\t= 16 %. `120. 5 \t\tDividend = 12% (`100) = `12 \t\tChoice (b): Rate of return = 50 \u00d7 5% \t\t \u2234 Choice (a) can be concluded. 60 \t\tRate=of return 11=220 (100)% 10% \t\t= 25 %. \t\tChoice (b) can be concluded. Choice (c) follows. 6 2\t 2.\t Total investment = `24,000 \t\tChoice (c): Rate of return = 60 \u00d7 6% = 36 %. 70 7 \t\tCost of each share = `300 \t\tChoice (d): Rate of return = 70 \u00d7 7% 80 \t\tNumber of shares bought = 24000 = 80 300 49 \t\tAnnual income\/share = `20 \t\t= 8 %. \t\tTotal annual income (in `) = (80)(20) = 1600. \t\t \u2234 The least attractive scheme is choice (1), since it Hints and Explanation the yields the least rate of return. \t23.\t Face value of each share = `300 \t\tDiscount\/share = `60 2\t 5.\t Face value of each share = `200 \t\tMarket value of each share (in `) = 300 \u2013 60 = 240 \t\tDividend rate = 8% per annum \t\tDividend rate = 6% per annum \t\t \u2234 Annual income per share \t\tDividend\/share = 6% of (`300) = `18 \t\t = 8% of (`200) = `16. Level 3 \t26.\t (i)\t Effective discount = Total discount \u00d7 100. 2\t 7.\t (i)\tFind the annual dividend from A and B. Total market value \t\t(ii)\tMV of share A = 100 + x. \t\t \tMV of share B = 100 \u2212 x \t\t(ii)\tLet the market value of each share be m. \t\t(iii)\tDividend from share A = x% of (100 + x), \t\t(iii)\tFV1 = 100m and FV2 = 100m where x% is the rate of return and (100 + x) is 100 + x 100 \u2212 x the MV. \t\t(iv)\tSimilarly, find dividend from share B. \t\t(iv)\tFind the total face value which is less than the \t\t(v)\tEquate total dividend in x to 10. total market value. \t\t(v)\tEffective discount = (Total FV \u2212 Total MV) \u00d7 100. Total FV","21.16 Chapter 21 \t28.\t Let the rates of returns from P, Q and R be \t\tFace value of each share (in=`) 8=4000 20 \t\t \u2234 f = 20 \t\tx%, y% and z% and x+y = z. 2 2\t 9.\t (i)\tFind the dividend received per share in each \t\t \u2234 m > f case. \t\t \u2234 Kiran bought each share above par. \t\t(ii)\tTotal dividend from share A is 8% of `4000. 3\t 4.\t Face value\/share = `100 \t\t(iii)\tTotal dividend from share B is 10% of `4800. \t\tPremium\/share = 20% of `100 = `20 \t30.\t (i)\tLet the investment of Ashok be `x in R and \t\tMarket value\/share (in `) = 100 + 20 = 120 equate the total dividend to `1550. \t\tTotal market value = `39,600 \t\t(ii)\tLet the investment on share R be `x. \t\tNumber of shares b=ought 3=91,26000 330 \t\t(iii)\t10% of 5000 + 8% of 7500 + 15% of x = 1550. 3\t 1.\t Let the rate of return that Lokesh gets be r%. The \t\tDividend rate = 6% per annum extra annual income of Lokesh = r\u2009% of (his extra \t\tAnnual income\/share = 6 (`100) investment). 100 \t\t\u2234240 = r (4800) \t\t = `6 100 \t\tTotal annual income (in `) = (330)(6) \u2234r = 5%. \t\t = 1980. 3\t 2.\t Since he has to spend more than the face value to purchase each share, r\u2009% < d%. \t35.\t Whenever a person buys all shares at par, the rate at which the dividend is paid to him is the rate of Hints and Explanation \t33.\t Market value of each share (i=n `) 1200 25 return that he receives. =48 \t\t \u2234 Rohit would be paid a dividend at 5%. \t\t\u2234 m = 25","1222CChhaapptteerr TKimineemaantidcsWork REmEmBER Before beginning this chapter, you should be able to: \u2022 Understand the time taken for each work we do \u2022 Know basic concepts of work \u2022 Explore the idea of increase in work-load in shorter time durations KEY IDEaS After completing this chapter, you should be able to: \u2022 Know the fundamental assumptions that are made while solving the problems on time and work \u2022 Understand the concept of man-days \u2022 Know about the sharing of the money earned \u2022 Find the time taken by pipes and cisterns to fill a tank Figure 1.1","22.2 Chapter 22 INTRODUCTION In this chapter, we will look at the relation between the amount of work done, the time taken to do that work and the number of people and their rates of doing work. The work may be constructing a wall or a road, filling up or emptying a tank (or a cistern) or eating a certain amount of food. This could be measured in any convenient unit. Quite often, the entire work mentioned can be taken as 1 unit. But this is not necessary. Time is measured in days, hours, etc. There are some basic assumptions that are made while solving the problems on Time and Work. These are taken for granted and are not specified in every problem. 1.\t I\u0007f a person (or one member of the workforce) does some work in a certain number of days, then we assume (unless otherwise explicitly stated in the problem) that he\/she does the work uniformly, i.e., he\/she does the same amount of work everyday. For example, if a person can complete a work in 15 days, we assume that he completes 1 of the work in 15 one day. If a person completes a piece of work in 4 days, we assume that he\/she completes 1 of the work on each day and conversely, if a person can complete 1 of the work in one 4 4 day, we assume that he can complete the total work in 4 days. 2.\t I\u0007f there is more than one person (or members of \u2018workforce\u2019) carrying out the work, it is assumed that each person (or members of the workforce), unless otherwise specified, does the same amount of work each day. This means that they share the work equally. If two people together can do the work in 8 days, it means that each person can complete it in 16 1 days. This, in turn, means that each person can do 16 of the work per day. In a number of problems, we find people working at different rates. We consider the following two examples: 1.\t \u0007If two persons A and B can individually do some work in 20 days and 30 days respectively, we can find out how much work can be done by them together in one day. Since A can do 1 1 20 part of the work in one day and B can do 30 part of the work in one day, both of them together can do \uf8ee 1 + 1\uf8f9 part of the work in one day. \uf8ef\uf8f0 20 30 \uf8fb\uf8fa 2.\t A\u0007 man works three times as fast as a boy does and the boy takes 12 days to complete a certain piece of work. If the boy takes 12 days to complete the work, then the man takes 1 only 4 days to complete the same work. Per day the boy does 12 of the work and the man does 1 , i.e., 3 of the work. If they work together, each day, \uf8eb1 + 3\uf8f6 or 1 of the work 4 12 \uf8ed\uf8ec 12 12\uf8f7\uf8f8 3 gets done or it takes 3 days for the work to be completed. From the above two examples, we can arrive at the following conclusion\/formula. I\u0007f A can do a piece of work in p days and B can do it in q days, then A and B together pq can complete the same in p+q days. We should recollect the fundamentals of variation (direct and inverse) here.","Time and Work 22.3 1.\t \u0007If the number of days is constant, work and men are directly proportional to each other, i.e., if the work to be done increases, more men are required to complete the work in the same number of days. 2.\t I\u0007f the number of men is constant, work and days are directly proportional, i.e., if the work increases, more days are required to complete the work. 3.\t \u0007If the work is constant, the number of men and days are inversely proportional, i.e., if the number of men increases, fewer days are required to complete the same work and vice-versa. The concept of man-days is very important and useful here. The number of men multiplied by the number of days for which they work is a measure of the work in man-days. The total number of man-days representing a specific task is constant. So, if we change one of the variable\u2014men or days, then the other will change accordingly, so that their product remains constant (remember from our knowledge of variation, two variables whose product is a constant, are said to be inversely proportional to each other). The two variables \u2018men\u2019 and \u2018days\u2019 are inversely proportional to each other, if the work to be done remains constant. Example 22.1 If 20 men take 30 days to complete a job, in how many days can 25 men complete the job? Solution If 20 men can complete the job in 30 days, then the work is 20 \u00d7 30 = 600 man-days. If this work is to be done by 25 men, then the number of days they take is 600 = 24. 25 Example 22.2 Fifteen men take 10 days to complete a job working 12 hours a day. How many hours a day should 10 men work to complete the same job in 20 days? Solution Since 15 men take 10 days working 12 hours per day, the total work done measured in terms of man-hours is 15 \u00d7 10 \u00d7 12. When 10 men are required to complete the same job in 20 days working h hours a day, work done = 10 \u00d7 20 \u00d7 h. But 10 \u00d7 20 \u00d7 h = 15 \u00d7 10 \u00d7 12. Hence, the number of hours for which they should work per day is 15 \u00d7 10 \u00d7 12 = 9. 10 \u00d7 20 \u2234 10 men can complete the work in 20 days working for 9 hours per day. Hence, in general we can say that: If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate), then M1D1H1 = M 2D2H2 . W1 W2","22.4 Chapter 22 Example 22.3 A piece of work can be done by 16 men in 8 days working 12 hours a day. How many men are needed to complete another work, which is three times the first one, in 24 days working 8 hours a day? Solution Using the formula, M1D1H1 = M 2D2H2 . W1 W2 Let W1 = x and W2 = 3x. M1 = 16, H1 = 12, D1 = 8 H2 = 8, D2 = 24. \u2234 16 \u00d7 8 \u00d7 12 = M2 \u00d7 24 \u00d7 8 x 3x \u21d2 M 2 = 24. \u2234 Required number of men is 24. Example 22.4 A can do a piece of work in 9 days and B can do the same in 12 days. In how many days can the work be completed if A and B work together? Solution 1 1 7 9 12 36 One day work of A and B = + = . So, they can complete the work in 36 , i.e., 5 1 days. 7 7 Example 22.5 A and B working together can do a piece of work in 12 days and A alone can complete the work in 18 days. How long will B alone take to complete the job? Solution 1 1 12 18 In a day, A and B together can do of the work. In a day, A alone can do of the work. \u2234 In one day, work done by B alone is 1 1 = 1 . = 12 \u2212 18 36 \u2234 B alone can complete the work in 36 days. Example 22.6 A and B working together can do a piece of work in 12 days, B and C can do it in 15 days and C and A can do the same work in 20 days. How long would each of them take to complete the job?","Time and Work 22.5 Solution 1 12 Work done by A and B in 1 day = . Work done by B and C in 1 day = 1 . 15 Work done by C and A in 1 day = 1 . 20 Adding all the three, we get the work done by 2(A + B+ C) in 1 day = 1 + 1 + 1 = 1 . 12 15 20 5 \u2234 A, B and C can together finish 1 of the work in 1 day. 10 \u2234 Work done by A in 1 day = Work done by A, B and C in 1 day \u2013 Work done by B and C in 1 day. = 1 \u2212 1 = 1 . 10 15 30 \u2234 A alone can do it in 30 days. Work done by B in 1 day = 1 \u2212 1 = 1 . 10 20 20 \u2234 B alone can do it in 20 days. Work done by C in 1 day = 1 \u2212 1 = 1 . 10 12 60 \u2234 C alone can do it in 60 days. Example 22.7 To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days. How long would each take to complete the work individually? Solution Given that, three times A\u2019s daily work = (B + C)\u2019s one day\u2019s work. \u21d2 (A + B + C)\u2019s daily work = four times A\u2019s daily work. But (A + B + C)\u2019s daily work = 1 . 5 \u2234 A\u2019s daily work = 1 ; A takes 20 days to do the work. 20 Also, given two times C\u2019s daily work = (A + B)\u2019s daily work \u21d2 three times C\u2019s daily work = (A + B + C)\u2019s daily work But (A + B + C)\u2019s daily work = 1 . 5","22.6 Chapter 22 \u2234 C\u2019s daily work = 1 ; C takes 15 days to do the work. 15 \u2234 B\u2019s daily work = 1 \u2212 \uf8eb 1 + 1\uf8f6 = 1 . 5 \uf8ed\uf8ec 20 15\uf8f8\uf8f7 12 \u2234 A, B and C working alone can complete the work in 20 days, 12 days and 15 days respectively. Example 22.8 If 4 men or 5 women can construct a wall in 82 days, then how long will it take for 5 men and 4 women to do the same work? Solution Given 4m = 5w, where m is the work done by one man in one day and w is the work done by one woman in one day. \u21d2 1m = 5w . 4 Now, 5m + 4w = 5 \uf8eb 5w \uf8f6 + 4w = 41w . \uf8ec\uf8ed 4 \uf8f8\uf8f7 4 If 5w can do the work in 82 days, then\u200941w \u2009can do in \uf8eb 5w \u00d7 82 \u00d7 4\uf8f6 days, i.e., 40 days. 4 \uf8ed\uf8ec 41w \uf8f7\uf8f8 Example 22.9 While 4 men and 6 boys can do a piece of work in 2 days, 1 man and 3 boys can do the same work in 6 days. In how many days can 1 man and 1 boy complete the same work? Solution Let the capacities of one man and one boy be m and b respectively. Given, 4m + 6b = 1 2 That is, 2m + 3b = 1 \b(1) 4 Also, m + 3b = 1 \b(2) 6 Eqs. (1) \u2212 (2) gives, m = 1 \u2212 1 = 1 4 6 12 On substituting \u2018m\u2019 in Eq. (2), we have b = 1 . 36 m + b = 1 + 1 = 1 . 12 36 9 \u2234 1 man and 1 boy can complete the work in 9 days.","Time and Work 22.7 Example 22.10 If X works 3 times as fast as Y and is able to complete a work in 40 days less than the number of days taken by Y, then find the time in which they can complete the work working together. Solution If Y does the work in 3 days, X does it in 1 day, i.e., the difference is 2 days. But the actual difference is 40 days. If difference is 2 days, X takes 1 day and Y takes 3 days. If difference is 40 days (i.e., 20 times), X takes 20 days and Y takes 60 days. \u2234 Time taken together = 20 \u00d7 60 = 15 days. 20 + 60 Example 22.11 A and B can do a piece of work in 10 days and 15 days, respectively. They started the work together but B left after sometime and A finished the remaining work in 5 days. After how many days (from the start) did B leave? Solution A\u2019s work for 5 days = 5 \u00d7 1 = 1 work. 10 2 The remaining half of the work was done by A and B together. Work done by A and B in a day = 1 + 1 = 1 . 10 15 6 1 \u2234 The number of days they worked together= 12= 3 days. 6 Hence, B left after 3 days from the day the work started. Example 22.12 A and B can do a piece of work in 6 days and 9 days respectively. They work on alternate days starting with A on the first day. In how many days will the work be completed? Solution Since they work on alternate days, let us consider a period of two days. In a period of two days, work done by A and B = 1 + 1 = 5 . 6 9 18 If we consider three such time periods (we consider 3 periods because in the fraction 5 , the numerator 5 goes three times in the denominator 18). 18 Work done = 3 \u00d7 \uf8eb 5 \uf8f6 = 15 . \uf8ec\uf8ed 18 \uf8f8\uf8f7 18","22.8 Chapter 22 Remaining work 1 \u2212 15 = 3 = 1 . 18 18 6 Now it is A\u2019s turn, since 3 whole number of periods are over. 1 Time taken by A to finish\u2009 6 \u2009of the work is one day. So, total time taken = (3 \u00d7 2) + 1 = 7 days. Example 22.13 P, Q and R can complete a job in 20 days, 30 days and 40 days respectively. They started working on it. Q and R left after working for certain number of days and P alone completed the remaining work 7 days. Find the time taken to complete the job (in days). (a) 12\t (b) 13\t (c) 14\t (d) 11 Solution Let the time taken to complete the job be t days. Job = (t \u2013 7) days of work of P, Q and R + 7 days of work of P = (t \u2212 7) \uf8eb 1 + 1 + 1 \uf8f6 + 7 \uf8eb 1 \uf8f6 \uf8ed\uf8ec 20 30 40 \uf8f7\uf8f8 \uf8ed\uf8ec 20 \uf8f8\uf8f7 (t \u2212 7) \uf8eb\uf8ed\uf8ec 13 \uf8f6 + 7 =1\u21d2 (t \u2212 7)(13) + 42 =1 120 \uf8f7\uf8f8 20 120 13(t \u2212 7) = 78 \u21d2 t = 13. Example 22.14 Y is thrice as efficient as Z who is half as efficient as X. X, Y and Z can complete a job in 25 days. Find the time in which X and Y can complete it (in days). (a) 30\t (b) 36\t (c) 40\t (d) 45 Solution Let the time in which X, Y and Z can complete the job be x days, y days and z days respectively. 1 = 3 \uf8eb 1\uf8f6 and 1 = 1 \uf8eb 1\uf8f6 . y \uf8ec\uf8ed z \uf8f7\uf8f8 z 2 \uf8ec\uf8ed x \uf8f7\uf8f8 \u2234y = z and x = z 3 2 1 + 1 + 1 = 1 x y z 25 2 + 3 + 1 = 1 \u21d2 z = 150. z z z 25 \u2234 y = 50 and x = 75. X and Y can complete it in (75)(50) days = 30 days. 75 + 50","Time and Work 22.9 Sharing of the Money Earned When a group of people do some work together and earn some money together for doing that work, this money has to be shared by all these people. In general, money earned is shared by people who worked together in the ratio of the total work done by each of them. 2 of the work, then he should get 2 of For example, let A and B complete a work. If A does 5 5 the total earnings due to the work. The remaining 3 \u2009of the work is done by B, then the remaining 5 3 5 of the earnings should be paid to B. When people work for the same number of days each, then the ratio of the total work done will be the same as the work done by each of them per day. Hence, if all the people involved, work for the same number of days, then the earnings can directly be divided in the ratio of work done per day by each of them. Example 22.15 A, B and C can do a piece of work in 4 days, 5 days and 7 days respectively. They get `415 for completing the job. If A, B and C have worked together to complete the job, what is A\u2019s share? Solution Since they work for the same number of days, the ratio in which they share the money is the ratio of the work done per day. That is, 1 : 1 : 1 = 35 : 28 : 20. 4 5 7 Hence, A\u2019s share is \uf8eb 35 \uf8f6 \u00d7 415 = `175. \uf8ed\uf8ec 83 \uf8f8\uf8f7 Example 22.16 The ratio of the efficiencies of X, Y and Z is 3 : 4 : 5. The total amount of wages of X, Y and Z working for 20 days, 10 days and 12 days respectively was `6400. Find the amount of their total wages, if X, Y and Z worked for 30 days, 15 days and 8 days respectively (in `). (a) 5700\t (b) 9500\t (c) 7600\t (d) 8550 Solution Ratio of daily wages of X, Y and Z = ratio of the efficiencies of x, y and z = 3 : 4 : 5. Let the daily wages of X, Y and Z be `3w, `4w and `5w respectively. 20(3w) + 10(4w) + 12(5w) = 6400 160w = 6400 w = 40. \u2234 Required total wage (in `) = 30(3w) + 15(4w) + 8(5w) = 190w = 7600.","22.10 Chapter 22 PIPES AND CISTERNS There can be pipes (or taps) filling or emptying tanks with water. The time taken by different taps (to fill or empty the tank) may be different. Problems related to these can also be dealt with in the same manner as the problems on work have been dealt with, so far in this chapter. There is only one difference between the problems on regular work (of the type seen earlier on in the chapter) and those in pipes and cisterns. In pipes and cisterns, a filling pipe or tap does positive work and an emptying pipe or a \u2018leak\u2019 does negative work. Example 22.17 Two pipes A and B can fill a tank in 12 minutes and 18 minutes respectively. If both the pipes are opened simultaneously, how long will they take to fill the tank? Solution 1 12 The part of the tank filled by A in 1 minute = . The part of the tank filled by B in 1 minute = 1 . 18 The part of the tank filled by both the pipes in 1 minute = 1 + 1 = 5 . 12 18 36 \u2234 The tank can be filled in 36 = 7 1 minutes. 5 5 Example 22.18 Pipe A can fill a tank in 12 minutes, pipe B in 18 minutes and pipe C can empty the full tank in 36 minutes. If all of them are opened simultaneously, find the time taken to fill the empty tank. Solution The work done by the 3 pipes together in 1 minute = 1 + 1 \u2212 1 = 4 = 1 . 12 18 36 36 9 So, the empty tank will be filled in 9 minutes. Example 22.19 Two taps P and Q which can independently fill a tank in 15 hours and 30 hours respectively were opened simultaneously, when the tank was empty. When the tank was half-full, an emptying tap R was opened. If the emptying tap R can empty the full tank in 20 hours, then in how much time will the tank be completely filled? (a) 12 hours\t (b) 15 hours\t (c) 18 hours\t (d) 20 hours Hints \u2009\u2009(i)\t Half of the tank is filled in 5 hours (ii)\t Let the time taken to fill the tank be x hours Use, x + x \u2212 (x \u2212 5) =1 and find x. 15 30 20","Time and Work 22.11 Example 22.20 Ten pipes are fitted to a tank. Some of these are filling pipes while the others are emptying pipes. Each filling pipe can fill the tank in 8 hours. Each emptying pipe can empty it in 16 hours. All the pipes are opened simultaneously. The tank takes 2 hours to be filled. How many filling pipes are fitted to it? Choose the correct answer from the following option. (a) 8\t (b) 7\t (c) 9\t (d) 6 Solution Let the number of filling pipes be f. Number of emptying pipes = 10 \u2013 f Part of the tank filled each hour = 1 . 2 \u2234 1 f \u2212 1 (10 \u2212 f )= 1 8 16 2 1 f \u2212 5 + f = 1 8 8 16 2 3f = 9 \u21d2 f = 6. 16 8","22.12 Chapter 22 TEST YOUR CONCEPTS Very Short Answer Type Questions \t1.\t A can read a book in x minutes. What part of the and C. If they got `900 for completing the work, book can he read in k minutes? then who receives more share in the earnings? \t2.\t Work done by A in 3 days is equal to the work 1\t 5.\t 12 men or 18 women can do a work in 16 days. In done by B in 4 days. What is the ratio of time how many days 12 men and 18 women can do the taken by A and B to complete a work? work? \t3.\t A can complete 2 of work in 6 days. In what time \t16.\t A, B and C can do a work in x, 3x and 5x days, 3 respectively. They worked together and earned `460. What is the share of B? can he complete 4 of the work? 9 \t17.\t A and B can do a work in 20 and 30 days, respec- tively. They completed the work in 10 days with \t4.\t A can do a work in x days and B can do the same the help of C. In how many days can C alone do work in y days. If x > y, then who can do more the work? work in 6 days? \t18.\t A can paint 6 walls in 5 days. B can paint 8 walls \t5.\t If x men can do a work in y days, 2x men can do (of the same area) in 4 days. Working together, the same work in 2y days. (True\/False) in how many days can they paint 48 walls (of the same area)? \t6.\t A is twice as good workman as B. A takes 6 days to complete a work. In what time can B complete 1\t 9.\t The ratio of efficiencies of A, B and C is 2 : 3 : 4. the work? Working together, they can complete a work in 20 days. In how many days can C alone finish the \t7.\t A and B together can do a work in 20 days, B and work? C can do the same work in 60 days. Who is the most efficient among A, B and C? \t20.\t On working 10 hours a day, 15 men can com- plete a piece of work in 20 days. In how many PRACTICE QUESTIONS \t8.\t A and B completed a work and divided the earnings days can 30 men complete it if they work 5 hours in the ratio of 2 : 3. What is the ratio of time taken per day? to complete the work by A and B, respectively? \t21.\t A and B can do a work in 20 days, B and C in \t9.\t 8 men can knit 8 baskets in 8 days. In how many 40 days, and A and C in 30 days. Who is the days can 3 men knit 3 baskets? most efficient among the three persons? \t10.\t 1 man can load 1 box in a truck in 5 minutes. How 2\t 2.\t A and B together can do a work in 18 days. A many full trucks can 8 men load in 45 minutes worked for 12 days with B and left the work. B given that the truck can hold 10 boxes? attended the work for 27 days and by that time the work gets completed. In how many days can B 1\t 1.\t Pipe A can fill a tank in 40 minutes. Pipe B can alone complete the work. empty the tank in 30 minutes. If both the pipes are opened simultaneously when tank is half full, then \t23.\t Work done by (x + 4) men in (x + 5) days is equal will the tank become full or empty? to the work done by (x \u2212 5) men in (x + 20) days. What is the value of x? 1\t 2.\t Pipe A can fill a tank in 2 hours at the rate of 6 litres per minute. What is the capacity of the tank? \t24.\t Pipe A can fill a tank in 15 hours Pipe A and Pipe B together can fill it in 10 hours Pipe B can fill \t13.\t If A and B can do a work in x and y days, respec- 8 litres per minute. Find the capacity of the tank. tively, then the time taken by A and B together to \t25.\t 18 men can construct 200 m long wall in 16 days working 9 hours per day. In how many days complete the work is x + y . (True\/False) can 36 men construct 500 m long wall working 2 6 hours per day? 1\t 4.\t A can do a work in 18 days. He worked for 10 days and left. The remaining work is completed by B","Time and Work 22.13 Short Answer Type Questions \t26.\t Vinay and Vikram can complete a work in 48 and 2 days, 10 men left. How many hours a day should 36 days, respectively. If they work on alternate days the remaining men work to complete it on time? beginning with Vinay, in how many days will the work be completed? 3\t 7.\t Time taken by A to complete a work is 7 days more than the time taken by B to complete the 2\t 7.\t A is twice as efficient as B. Time taken by B to same work. Working together they can complete 4 the work in 12 days. In what time can A alone complete 7 part of the work is 6 days more than complete the work? the time taken by A to complete 3 part of the 3\t 8.\t A is 20% more efficient than B. B can do a piece of 7 work in 20 days. In how many days can A do the same work. In how many days can A alone do the same work? work? 3\t 9.\t Three men or five women can complete a piece of work in 8 days. In how many days can 6 men and 2\t 8.\t The ratio of work efficiency of a man and a woman 6 women complete it? is 3 : 2. A woman can do a work in 30 days. In how many days can 4 men and 4 women do the \t40.\t A certain number of men completed a job in work? 10 days. If there were 5 more men, it could have been completed in 8 days. How many men will be 2\t 9.\t 12 men or 15 women can do a work in 40 days. required to complete it in 5 days? 8 men and 10 women can do the work in how many days? \t41.\t Two pipes A and B can fill a tank in 20 and 24 minutes, respectively. Pipe C can empty the \t30.\t 12 men and 15 women can do a work in 6 days, tank in 10 minutes. Pipes A and B are opened and 6 men and 12 women can do it in 10 days. In for 5 minutes and then pipe C is also opened. In how many days can 8 men and 10 women do the what time can the tank become full or empty after same work? opening pipe C? \t31.\t Certain sum is sufficient to pay wage to A for \t42.\t A can complete a piece of work in 15 days. B 15 days or to B for 30 days. For how many days is can complete it in 10 days. With the help of C, the sum sufficient to pay both A and B? they can complete it in 4 days. They all worked together and earned a total of `750. Find C\u2019s share. \t32.\t A, B and C can do a work in 20, 25 and 30 days, PRACTICE QUESTIONS respectively. They together started the work, but B \t43.\t Time taken by 8 men and 6 boys is 3 times the and A left the work 7 days and 4 days, respectively time taken by 15 men and 30 boys to complete a before completion of the work. How many days work. If 8 men and 12 boys can do a work in 34 did C work for? days, then how many men can do it in 17 days? 3\t 3.\t Anand is 50% more efficient than Bharath and 4\t 4.\t Prakash, Rohit and Sameer can complete a job Bharath is 100% more efficient than Chandu. in 1 day, 20 days and 10 days, respectively. They Working together, they can complete a work in started the job but Prakash was unwell on the first 10 days. In how many days can Anand alone do day, he could not work at his full capacity and the work? Prakash left after a day. The other two completed the job. Rohit was paid `17,000 out of the total of 3\t 4.\t Three hundred men can construct a 200 m long `60,000 paid to them. At what percentage of his wall in 12 days working 8 hours a day. In how full capacity, did Prakash work on the first day? many days can 120 men construct 180 m long wall working 9 hours per day? \t45.\t Pipe A and pipe B can fill a tank in 24 minutes and 28 minutes, respectively. If both the pipes are 3\t 5.\t A, B and C can complete a piece of work in opened simultaneously, then after how many min- 4 days, 8 days and 12 days, respectively. They utes should pipe B be closed such that the tank worked together and earned a total of `660. Find becomes full in 18 minutes? B\u2019s share (in rupees). 3\t 6.\t Thirty men can dig a well in 10 days on work- ing 8 hours a day. They started the work but after","22.14 Chapter 22 Essay Type Questions \t46.\t In a group, there were M men. They started work- 4\t 9.\t 10 women can complete a job in 12 days. 4 of ing on a job of 330 units. Each man could do them started working on the job. After every 1 unit in 1 day. After each day of work, a man of 4 days, a woman joined the group. Every woman the same efficiency as each man in the group join joining the group has equal capacity as any woman the group. The job was completed at the end of in the group. Find the time taken to complete the 11 days. Find M. job. (In days). 4\t 7.\t Ram and Shyam can complete a job in 20 days if \t50.\t Prakash, Ramesh and Suresh started a job. After they work together. If they complete it by work- 2 days, Prakash left. After another 2 days Ramesh ing on alternate days, in how many days will it be left. In another 2 days, Suresh completed the completed? remaining part of the job. If Prakash can complete the same work in more than 6 days and Ramesh 4\t 8.\t A, B and C can complete a job in 20 days, can complete it in more than 12 days, who got the 30 days and 40 days, respectively. They worked for highest share of the wages? 6 days and then A left. B and C completed the job. Find B\u2019s wages in the total wages of `20,000 paid to them. (in `) CONCEPT APPLICATION Level 1 \t1.\t A is thrice as efficient as B. A and B can complete a \t5.\t Where 6 men and 9 women can complete a piece piece of work in 12 days. Find the number of days of work in 10 days. What is the time taken by 4 in which A alone can complete it. men and 6 women to complete it? \t\t(a) 48\t\t (b) 16 \t\t(a) 10 days\t\t (b) 12 days \t\t(c) 20\t\t (d) 32 \t\t(c) 15 days\t\t (d) 18 days PRACTICE QUESTIONS \t2.\t A and B can complete a piece of work in 15 days \t6.\t A and B can complete a piece of work in 12 days. and 10 days, respectively. They work together for B and C can complete it in 24 days. A and C can 4 days and then B leaves. In how many days will A complete it in 16 days. In how many days can B alone complete the remaining work? alone complete it? \t\t(a) 6\t\t (b) 8 \t\t(a) 16\t\t (b) 32 \t\t(c) 5\t\t (d) 10 \t\t(c) 12\t\t (d) 20 \t3.\t Sunny can complete a piece of work in 30 days. \t7.\t A can do a piece of work in 34 days. He worked He worked for 6 days and left. Bunny completed for 14 days and then left. B completed the remain- the remaining work in 16 days. In how many days ing work in 30 days. In how many days can B can the entire work be completed if they work alone complete the work? together? \t\t(a) 38\t\t (b) 51 \t\t(a) 8\t\t (b) 12 \t\t(c) 16\t\t (d) 20 \t\t(c) 46\t\t (d) 62 \t4.\t B is twice as efficient as A, who works half as fast as \t8.\t Certain men can do a piece of work in 22 days. C. If A, B and C can complete a piece of work in If the number of men decreases by 55, then they 20 days. In how many days can B and C together will take 11 days more to complete the same work. complete it? Find the number of men present initially. \t\t(a) 50\t\t (b) 100 \t\t(a) 165\t\t (b) 155 \t\t(c) 25\t\t (d) 30 \t\t(c) 185\t\t (d) 175","Time and Work 22.15 \t9.\t Pipe A can fill a tank in 20 minutes and pipe B 1\t 6.\t A piece of work can be done by 64 men in 17 days can fill the tank in 30 minutes. Both the pipes can fill at the rate of 8 litres per second. What is the working for 9 hours per day. In how many days capacity of the tank (in litres)? 8 can 34 men do a piece of work 3 times of the \t\t(a) 5670\t\t (b) 6570 previous one on working 8 hours per day? \t\t(c) 6750\t\t (d) 5760 \t\t(a) 92\t\t (b) 98 1\t 0.\t A, B and C can do a piece of work in 8, 16 and \t\t(c) 96\t\t (d) 94 24 days, respectively. They work together and earn `528. What is the share of B? \t17.\t P and Q can do a piece of work in 12 and 16 days, respectively. With the help of R, they completed \t\t(a) `144\t\t (b) `152 the work in 5 days and earn `912. What is the share of R? \t\t(c) `176\t\t (d) `168 \t\t(a) `249\t\t (b) `247 \t11.\t A works three times as fast as B. B takes 56 days \t\t(c) `243\t\t (d) `245 more than A to complete a work. Working together in how many days can they complete the 1\t 8.\t A piece of work can be done by 9 men and 15 work? women in 24 days. In how many days can 15 men and 15 women do the same work? \t\t(a) 24\t\t (b) 21 \t\t(a) 6\t\t (b) 12 \t\t(c) 27\t\t (d) 29 \t\t(c) 9\t\t (d) 15 1\t 2.\t A, B and C can complete a piece of work in 25, 30 and 50 days, respectively. They started the work 1\t 9.\t A piece of work can be done by 12 men in 24 together but A and C left 2 days before the com- pletion of the work. In how many days will the days. After 4 days, they started the work and then 6 work be completed? more men joined them. How many days will they all take to complete the remaining work? \t\t(a) 14\t\t (b) 12 \t\t(a) 12 1 \t\t (b) 13 1 3 3 \t\t(c) 18\t\t (d) 10 11 2 13 2 PRACTICE QUESTIONS 1\t 3.\t When 6 men and 8 women can do a piece of work \t\t(c) 3 \t\t (d) 3 in 15 days, then 11 men and 16 women can do the same work in 8 days. In how many days can 4 men \t20.\t A and B can complete a piece of work in 4 days and 4 women do the work? and 8 days, respectively. They work on alternate days and A starts the work. In how many days will \t\t(a) 28\t\t (b) 24 the work be completed? \t\t(c) 36\t\t (d) 30 \t\t(a) 3\t\t (b) 4 1\t 4.\t A and B can do a piece of work in 12 days, B and \t\t(c) 5\t\t (d) 6 C in 15 days and A and C in 20 days. In how many days can each alone do the work? 2\t 1.\t X and Y can do a piece of work in 4 and 6 days, respectively. If Y works on the first day and they \t\t(a) 30, 20, 50\t (b) 30, 45, 60 work on alternate days, in how many days will twice the amount of work be completed? \t\t(c) 30, 20, 60\t (d) 20, 30, 50 9 2 10 2 1\t 5.\t P and Q can complete a certain work in 28 days \t\t(a) 3 \t\t (b) 5 and 56 days, respectively. P works for 7 days, and then Q joins P. In how many more days, can they \t\t(c) 9 1 \t\t (d) 9 1 complete the work? 5 2 \t\t(a) 7\t\t (b) 14 \t22.\t Three machines P, Q and R can do a piece of work in 7, 9 and 10 days, respectively. Due to a problem \t\t(c) 21\t\t (d) 28 in P and Q, they are working only at 70% and 90%","22.16 Chapter 22 of their efficiency, respectively. In how many days \t\t(a) 10\t\t (b) 20 can P, Q and R together do the work? \t\t(c) 15\t\t (d) 25 2 1 \t\t(a) 1 3 days\t\t (b) 2 3 days \t27.\t If P can produce 60 cakes in 9 days and Q can produce 70 cakes in 21 days, how many days \t\t(c) 2 2 days\t (d) 3 1 days will they take to produce 100 cakes if they work 3 3 together? 2\t 3.\t A, B and C can complete a piece of work in 10 \t\t(a) 8\t\t (b) 9 days, 20 days and 25 days, respectively. If they take 40 days to complete a piece of work, then in how \t\t(c) 10\t\t (d) 11 many days can C alone complete the work? \t28.\t 15 men and 25 women can dig an area of 880 m2 \t\t(a) 65 days\t\t (b) 76 days in 8 days. In how many days can 20 men and 12 women dig an area of 1040 m2, if each man can \t\t(c) 95 days\t\t (d) 190 days dig twice the area that each woman can dig in the same amount of time? 2\t 4.\t A group of 5 people can do a piece of work in certain number of days. If 4 more people join the \t\t(a) 6 days\t\t (b) 8 days group, they take 12 days less to do the same work. In how many days can a group of 3 people do the \t\t(c) 10 days\t\t (d) 2 days work? \t29.\t P and Q can do a piece of work in 10 days and \t\t(a) 30\t\t (b) 45 35 days, respectively. If they work on alternate days beginning with Q, in how many days will the \t\t(c) 15\t\t (d) 60 work be completed? 2\t 5.\t A and B can complete a piece of work in 10 days and 12 days, respectively. If they work on alternate \t\t(a) 15 4 \t\t (b) 15 5 7 7 days beginning with B, in how many days will the work be completed? 4 5 7 7 \t\t(a) 10 5 \t\t (b) 11 \t\t(c) 16 \t\t (d) 14 6 PRACTICE QUESTIONS \t\t(c) 12 1 \t\t (d) 13 \t30.\t Ram, Shyam and Tarun are three people in a job. 3 Each takes m times the time taken by other two, to complete a job. Find m. \t26.\t A, B and C can complete a piece of work in 27 days, 36 days and 45 days, respectively. B and C \t\t(a) 1\t\t (b) 2 started the work. After 11 days, A joined them. If B left 12 days before its completion, in how many \t\t(c) 1 \t\t (d) None of these days will the work be completed? 2 Level 2 \t31.\t Anoop can complete a piece of work in 10 days found that the tank was full at 3:00 pm. At what working for 8 hours a day. Swaroop can complete time was Q shut? it in 12 days working 10 hours a day. How many days will they take to complete it if they work \t\t(a) 10:00 am\t (b) 12:00 noon 12 hours a day? \t\t(c) 1:00 pm\t\t (d) 2:00 pm \t\t(a) 4\t\t (b) 6 3\t 3.\t Anand completed one-fifth of a piece of work in 4 days. He was then assisted by Bhargav and they \t\t(c) 8\t\t (d) 10 completed the remaining work in 8 days. Bhargav can complete the work in _____ days. 3\t 2.\t Two taps P and Q can fill a tank in 12 hours and 18 hours, respectively. Both taps were opened at \t\t(a) 12\t\t (b) 16 7:00 am and after some time, Q was closed. It was \t\t(c) 20\t\t (d) 24","Time and Work 22.17 \t34.\t P works 25% more efficiently than Q and Q works time taken by the other pair to complete the work. 50% more efficiently than R. To complete a cer- Which is the second pair? tain project, P alone takes 50 days less than Q. If in this project P alone works for 60 days and then Q \t\t(a) P, S\t\t (b) P, R alone works for 125 days, then in how many days can R alone can complete the remaining work? \t\t(c) Q, R\t\t (d) Q, S \t\t(a) 50\t\t (b) 75 4\t 0.\tThere are 25 workers in a group. Each can do 1 unit\/day. They start a job of 330 units. After \t\t(c) 100\t\t (d) 150 each day, a worker of the same efficiency as each worker in the group joins the group. The job was 3\t 5.\t A man takes 80 days to complete a job. To complete completed in x days. Find x. this job, 4 men, 8 women and 4 machines take 5 days. Alternatively, 4 men, 1 woman and 2 machines \t\t(a) 9\t\t (b) 10 take 10 days to complete the job. Find the time taken by a woman to complete the job (in days). \t\t(c) 11\t\t (d) 12 \t\t(a) 90\t\t (b) 100 \t41.\t P, Q and R together can complete 50% of a work in 2 days. All three start the work but after two days \t\t(c) 105\t\t (d) 120 Q left. P and R completes one-sixth of the work in the next day and then P leaves. The remaining \t36.\t Two taps A and B, can fill a tank in 10 minutes work is done by R alone in 8 days. In how many and 15 minutes, respectively. In how many min- days can P alone can complete the work? utes will the tank be full if B was opened 3 minutes after A was opened? \t\t(a) 6\t\t (b) 8 \t\t(a) 4.2\t\t (b) 6.2 \t\t(c) 10\t\t (d) 12 \t\t(c) 7.2 \t\t (d) 8.2 4\t 2.\t A and B are two taps which can fill a tank in 6 hours and 9 hours, respectively. C is an emptying \t37.\t Two men are as efficient as 3 women who are as effi- tap, which can empty the tank in 7.5 hours Tap B cient as 4 machines. The number of men, women and machines are in the ratio of 3 : 4 : 5 and they is opened 3 hours after tap A is opened. For how have completed a job. They are paid a total of `4900 for it. Find the total share of women. (in `) long does tap C to be kept open if the tank has to be filled in 6 hours? PRACTICE QUESTIONS \t\t(a) 1 1 hours\t(b) 2 1 hours 2 2 \t\t(a) 1200\t\t (b) 1800 \t\t(c) 2400\t\t (d) 1600 \t\t(c) 3 hours\t\t (d) 5 hours 3\t 8.\t There are ten taps fitted to a tank. The filling taps 4\t 3.\t Anand, Raju, Suresh and Venkat together pro- that are filling the tank are five in number and duced 392 pieces of an item in 6 hours Suresh is each tap takes 5 hours to fill the tank. The empty- four times as efficient as Anand and is one\u2013third ing taps are also five in number each tap takes 6 less efficient than Venkat. Raju is half as efficient as hours to empty the tank. In how many hours can Venkat. How many pieces would Raju have pro- the empty tank be filled, if all the taps are opened duced, if he worked for 8 hours? simultaneously? \t\t(a) 84\t\t (b) 112 \t\t(a) 6\t\t (b) 5 \t\t(c) 28\t\t (d) 56 \t\t(c) 10\t\t (d) 12 4\t 4.\t A worker has to complete a job of 175 units. On each day starting from the second, he does 75% of 3\t 9.\t P can complete a piece of work in 3 days. Q takes the part of the job he did on the previous day. Find triple the time taken by P, R takes 4 times that the number of days in which the job is completed taken by Q and S takes double the time taken by if he did 36 units of work on the 3rd day. R to complete the same task. They are grouped into two pairs. One of the pairs takes 2\u200921 times the \t\t(a) 3\t\t (b) 4 \t\t(c) 5\t\t (d) 6","22.18 Chapter 22 \t45.\t A is twice as good a workman as B. A takes 6 days \t\t(a) 8\t\t (b) 7 to complete a task. What time does B take to com- plete the work (in days)? \t\t(c) 6\t\t (d) 5 \t\t(a) 3\t\t (b) 6 4\t 8.\t Five men or ten women can complete a job in 20 days. Find the time in which four men and four \t\t(c) 9\t\t (d) 12 women can complete it (in days). 4\t 6.\t 27 men can dig a well in 20 days working 5 hours \t\t(a) 15\t\t (b) 20 a day. They start digging it. After 4 days, 12 men 1 2 leave. How many hours a day should the remaining \t\t(c) 13 3 \t\t (d) 16 3 men work to complete digging it by the scheduled date? \t49.\t A can do a task in 18 days. He works for 10 days and leaves. The remaining work is completed by B \t\t(a) 6\t\t (b) 8 and C. If they get `9000 for completing the work, then who receives more share in the earnings? \t\t(c) 10\t\t (d) 9 \t47.\t One man can load 1 box in a truck in 5 minutes. \t\t(a) C\t\t (b) A How many full trucks can 8 men load in 45 min- utes given that the truck can hold 10 boxes? \t\t(c) B\t\t (d) Cannot say Level 3 \t50.\t There are 4 people who can complete a work in 5\t 3.\t Eswar and Harish take 12 days and 16 days, 19 days individually. The work is started by one respectively to complete a job. Ganesh is atleast of the people on the first day. Everyday one more as efficient as Harish but almost as efficient as person joins and starting from the 4th day, all of Eswar. Ganesh and Harish work on alternate days the 4 people work together. In how many days, and completed the job in x days. Which of the will the work be completed? following can be the value of x? \t\t(a) 6 1 days\t (b) 6 1 days \t\t(a) 8\t\t (b) 12 4 19 PRACTICE QUESTIONS \t\t(c) 14\t\t (d) 17 1 \t\t(c) 7 days\t\t (d) 7 19 days \t54.\t Pipes X, Y and Z are fitted to a tank. Each of Y and Z can fill the tank in 6 hours. The efficiency \t51.\t The ratio of the efficiency of P, Q and R is 2 : 3 : of X, which is an emptying pipe, is half of Y. If X is fitted at one fourth of the height of tank from the 5. The total wages of P, Q and R working for 14, base and all the pipes are opened simultaneously, the tank would be filled in _______ hours. 24 and 20 days, respectively are `6000. Find the total wages of the three, if P works for 9 days, Q for 14 days and R for 8 days. 1 2 \t\t(a) `3000\t\t (b) `2860 \t\t(a) 4\t\t (b) 3 \t\t(c) `2450\t\t (d) `3240 \t\t(c) 3 1 \t\t (d) 3 2 \t52.\t Amar, Bhavan and Chetan can make a total of 8 dosas in one minute. They have to make a total of 5\t 5.\t X works four times as fast as Y. Y takes 60 days 80 dosas. Amar started making dosas. After some time, Bhavan and Chetan took over and completed more than X to complete a job. Find the time in the job. If it took a total of 20 minutes to complete the job and Amar made atleast 5 dosas per minute, which X and Y working together can complete how long did Amar work alone (in minutes)? the job (in days)? \t\t(a) 20\t\t (b) 10 \t\t(a) 9\t\t (b) 10 \t\t(c) 16\t\t (d) 12 \t\t(c) 11\t\t (d) 12 5\t 6.\t One man and 7 women can complete a job in 16 days. 19 men and 10 women can compete it","Time and Work 22.19 in 3 days. Find the time in which 6 men and 6 \t62.\t Amar, Bhavan and Chetan can complete a job in women can complete it (in days). 24 days, 36 days and 48 days, respectively. Amar, Bhavan and Chetan started it. After 6 days, Amar \t\t(a) 8\t\t (b) 6 left. The other two continued to work. Bhavan left 15 days before the completion of the job. Chetan \t\t(c) 9\t\t (d) 12 completed the remaining work. Find the total time taken to complete the job. (in days) 5\t 7.\t M and N can complete a job in 18 days and 20 days, respectively. They worked on it on alterna- \t\t(a) 21\t\t (b) 24 tive days starting with M. Find the time taken to complete it (in days). \t\t(c) 27\t\t (d) 30 \t\t(a) 18 9 \t\t (b) 19 \t63.\t There are 5 men in a group. Each man can com- 10 plete a job in 35 days. One of them starts it. Starting from the second day, a man joins until \t\t(c) 18 3 \t\t (d) 18 3 the 5th day. Thereafter all the men work together. 5 10 Find the total time taken to complete the job. (in days) \t58.\t Ganesh, Harish, Suresh and Mahesh worked together to produce 558 pieces of an item in \t\t(a) 9\t\t (b) 8 12 hours. Ganesh is twice as efficient as Harish and is five-sixth as efficient as Mahesh. Mahesh is \t\t(c) 10\t\t (d) 7 thrice as efficient as Suresh. How many pieces can Mahesh produce in 9 hours? \t64.\t A job can be completed by 2 men, 3 women and 4 children in 15 days. The same work can be \t\t(a) 144\t\t (b) 162 completed by 9 men and 6 children in 10 days. If 1 man and 1 woman can complete it in 48 days. \t\t(c) 126\t\t (d) 180 Find the time in which one man can complete it. (in days) 5\t 9.\t The efficiency of A, B and C is the same. They started working on a certain job. After 5 days A \t\t(a) 60\t\t (b) 75 leaves, after 5 more days B leaves and C completes the remaining work in 5 more days. Find the time \t\t(c) 80\t\t (d) 90 taken by each of them alone to complete the job. (in days) \t65.\t Mohan can complete a job in 8 days working PRACTICE QUESTIONS 9 hours a day. Sohan can complete it in 9 days \t\t(a) 25\t\t (b) 30 working 10 hours a day. In how many days can Mohan and Sohan together complete it working 8 \t\t(c) 40\t\t (d) 45 hours a day? 6\t 0.\t 18 men and 36 women can level an area of \t\t(a) 6\t\t (b) 4 810 sq. m. in 6 days. The ratio of the areas that each man and each woman can level in the same \t\t(c) 3\t\t (d) 5 amount of time is 3 : 1. Find the number of days in which 22 men and 14 women can level an area 6\t 6.\t Kiran and Pavan can complete a job in 40 days and of 1200 sq. m. 50 days, respectively. They worked on alternative days to complete it. Find the minimum possible time \t\t(a) 8\t\t (b) 12 in which they could have completed it. (in days) \t\t(c) 9\t\t (d) 10 2 1 5 2 6\t 1.\t There are 15 workers in a group. Each can do \t\t(a) 44 \t\t (b) 44 1 unit per day. All the workers started a job of 220 units. After each day, a worker who can do 1 unit \t\t(c) 44 3 \t\t (d) 44 4 per day joined the group. Find the time taken to 5 5 days). \t67.\t Pipes A, B and C are fitted to a tank. Each of A \t\t(a) 11\t\t (b) 12 and B can fill a tank in 9 hours. C is an emptying pipe which can empty it in 12 hours. It is fitted at \t\t(c) 13\t\t (d) 10","22.20 Chapter 22 one-third the height of the tank above the base. All Z is an emptying pipe which can empty the tank pipes are opened simultaneously. Find the time in in 9 hours. All the pipes are opened simultaneously which the tank will be filled (in hours). when the tank is half full. The tank would be \t\t(a) 5\t\t (b) 5 1 \t\t(a) filled in 72 hours. 2 \t\t(b) emptied in 72 hours. \t\t(c) 6.3\t\t (d) 6 1 2 \t\t(c) filled in 36 hours. \t68.\t P can complete a job in 60 days while Q can com- \t\t(d) emptied in 36 hours. plete it in 90 days. With the help of R, they com- 7\t 0.\t P, Q and R can complete a job in 6 days, 9 days and 12 days, respectively. They worked together pleted it in 20 days. If they earned a total of `3600, and completed it. They earned a total of `2600. Find P\u2019s share. (in `) then find R\u2019s share. (in `) \t\t(a) 1350 \t\t(a) 1360\t\t (b) 1600 \t\t(b) 1500 \t\t(c) 900 \t\t(c) 1480\t\t (d) 1540 \t\t(d) 1200 6\t 9.\t Pipes X, Y and Z are fitted to a tank. X and Y can fill a tank in 18 hours and 24 hours, respectively. PRACTICE QUESTIONS","Time and Work 22.21 TEST YOUR CONCEPTS Very Short Answer Type Questions \t1.\t k \t13.\t False x \t14.\t A 1\t 5.\t 8 days \t2.\t 3 : 4 1\t 6.\t `100 1\t 7.\t 60 days \t3.\t 4 days \t18.\t 15 \t19.\t 45 days \t4.\t B 2\t 0.\t 20 \t21.\t A \t5.\t False \t22.\t 45 days \t23.\t 20 \t6.\t 12 days 2\t 4.\t 14400 litres 2\t 5.\t 30 \t7.\t A \t8.\t 3 : 2 \t9.\t 8 days 1\t 0.\t 7 trucks \t11.\t empty \t12.\t 720 litres Shot Answer Type Questions \t26.\t 41 1 3\t 6.\t 12 4 3\t 7.\t 28 8 2 \t27.\t 5 days \t38.\t 16 2 3 2\t 8.\t 3 3\t 9.\t 2.5 2\t 9.\t 30 \t40.\t 40 \t30.\t 9 4\t 1.\t 55 minutes ANSWER KEYS \t31.\t 10 4\t 2.\t `250 3\t 2.\t 12 \t43.\t 34 3\t 3.\t 20 4\t 4.\t 15% \t34.\t 21 \t45.\t 7 3\t 5.\t 180 Essay Type Questions \t49.\t 20 5\t 0.\t Suresh \t46.\t 25 4\t 7.\t 40 \t48.\t 8000","22.22 Chapter 22 CONCEPT APPLICATION Level 1 \t 1. (b) \t 2. (c)\t 3. (b)\t 4. (c)\t 5. (c)\t 6. (b)\t 7. (b)\t 8. (a)\t 9. (d)\t 10. (a) \t11. (b)\t 12. (b)\t 13. (b)\t 14. (c)\t 15. (b)\t 16. (c)\t 17. (b)\t 18. (c)\t 19. (b)\t 20. (c) \t21. (a)\t 22. (d)\t 23. (d) \t 24. (b)\t 25. (b)\t 26. (b)\t 27. (c)\t 28. (c)\t 29. (b)\t 30. (b) Level 2 33. (c)\t 34. (b)\t 35. (d)\t 36. (c)\t 37. (d) \t 38. (a)\t 39. (a)\t 40. (c) 43. (b)\t 44. (b)\t 45. (d)\t 46. (d) \t 47. (b)\t 48. (d) \t 49. (b) \t31. (a)\t 32. (c)\t \t41. (b)\t 42. (b)\t Level 3 \t50. (a)\t 51. (a)\t 52. (b)\t 53. (c)\t 54. (b)\t 55. (c)\t 56. (a)\t 57. (a)\t 58. (b)\t 59. (b) \t60. (d)\t 61. (a)\t 62. (b)\t 63. (a)\t 64. (c)\t 65. (d)\t 66. (a)\t 67. (c)\t 68. (b)\t 69. (d) \t70. (d) ANSWER KEYS","Time and Work 22.23 CONCEPT APPLICATION Level 1 \t1.\t A = 3B and (A + B)\u2019s one day\u2019s work is equal to 1\t 7.\t Find what part of the work is done by P and Q in 4 days work by B. 5 days. The remaining work is done by R. \t2.\t Find the work done by A and B together and 1\t 8.\t Convert 15M + 15W into one variable, i.e., M or W and proceed. proceed. \t3.\t Sunny\u2019s 6 day\u2019s work is 6 \u00d7 1 = 1 . Remaining \t19.\t (i)\tThe work of 12 men in 4 days = 1 . 30 5 6 work is completed by Bunny in 16 days. \t\t(ii)\tAfter four days, 12 men can do remaining \t\tSo, Bunny\u2019s one day\u2019s work is 1 . work in (24 \u2212 4) days. 20 \t \t \t\u21d2 M1 = 12 and D1 = 20. C \t4.\t Given, B = 2A and A = 2 . \t\t(iii)\tM2 = (12 + 6), find D2 by using M1D1 = M2D2. \t5.\t Work done by (2 men + 3 women) is 30 days is \t20.\t Find the work done by A and B in a period of equal to the work done by (4 men + 6 women) in 2 days and proceed. d days. Find d. 2\t 1.\t Find the work done by X and Y in a period of two \t6.\t Find the work done by A + B + C in one day and days. proceed. \t\t(i)\tThe amount of work done by P and Q in one \t7.\t Find the work done by A in 14 days and then find day is 70% of 1 and 90% of 1 . the remaining work and proceed. 7 9 \t8.\t M1D1 = M2D2. \t\t(ii)\tThe amount of work done by P and Q in one Hints and Explanation \t9.\t Find the part of the tank filled in one minute by A day is 70% of 1 and 90% of 1 respectively. and B together and proceed. 7 9 1\t 0.\t Money is distributed according to their efficiencies. \t\t(iii)\tNow find the part of work done by P, Q and R in one day and proceed. \t11.\t Consider A = 3B and if A does the work in n days, 2\t 3.\t (i)\tThe ratio of capacities of A, B and C is 10 : 5 : 4. then B will do it in 3n days. 3n \u2013 n = 56 days. \t\t(ii)\tFind the time taken by A, B and C together to 1\t 2.\t Consider the number of days as x. A and C worked complete the work (say d). for (x \u2013 2) days. \t\t(iii)\tWhen they are taking d days, C alone takes \t13.\t Use M1D1 = M2D2. 25 days. 1\t 4.\t Calculate the work done by (A + B + C) in one \t\t(iv)\tFind how many days C alone takes if they day and proceed. complete the work in 40 days. \t15.\t (i)\tFrame the equations and solve. 2\t 4.\t (i)\tUse, M1D1 = M2D2. \t\t(ii)\tLet five people do the piece of work in x days. \t\t(ii)\tP works for 7 days, remaining work 7 3 Find x. = 1\u2212 28 = 4 . \t\t(iii)\t5(x) = 9(x \u2212 12) \t\t(iii)\tLet the required number of days = x. \t\t(iv)\tLet three people do the same work in y days. \t\t \t\u2234 x + x = 3 . \t\t(v)\tUse, 5 \u00d7 x = 3 \u00d7 y and find y. 28 56 4 2\t 5.\t Find the work done by A and B in a period of days \t16.\t M1D1H1 = M 2D2H2 . and proceed. W1 W2","22.24 Chapter 22 \t26.\t (i)\tConsider the total number of days as \u2018x\u2019. A, B \t\t(ii)\tFirst of all find the part of the work done by Q and C works for (x \u2013 11), (x \u2013 12) and x days and P in a period of 2 days. respectively. \t\t(iii)\tThen find total number of such periods \t\t(ii)\tLet A, B and C work for (x \u2013 11), (x \u2212 12) and (integer) required. x days respectively. \t\t(iv)\tThen find the time taken to complete remain- \t\t(iii)\tAdd the total work done by each of them and ing part starting with Q and then P. equate it to 1 and find x. 3\t 0.\t (i)\tFrame equations and solve. \t27.\t (i)\tFind the number of cakes produced by both of them in a day and proceed. \t\t(ii)\tLet the capacities or work completed in one \t\t(ii)\tFrom the given data find the number of days P day by the three people be 1 , 1 and 1 . and Q require to produce 100 cakes. R S T \t\t(iii)\tConsider 100 cakes as 1 unit and then proceed \t\t \tTake 1 = 1 \uf8eb 1 + 1 \uf8f6 , in general way. R m \uf8ec\uf8ed S T \uf8f8\uf8f7 2\t 8.\t (i)\t(15M + 25W )8 = (20M + 12W )d . 880 1040 \t\t \t 1 = 1 \uf8eb 1 + 1 \uf8f6 and 1 = 1 \uf8eb 1 + 1 \uf8f6 . \t\t(ii)\tFind d using 1M = 2W. S m \uf8ec\uf8ed T R \uf8f8\uf8f7 T m \uf8ec\uf8ed R S \uf8f7\uf8f8 \t29.\t (i)\tFind the work done by P and Q in one day \t\tAdd the above three equations and find m. and proceed. Level 2 \t31.\t (i)\tAnoop and Swaroop can complete a piece of \t\t(ii)\tLet the efficiency of R be 100. work in 80 and 120 hours respectively. Hints and Explanation \t \t \t\u2234 Efficiency of Q = 150 and Efficiency of P = \t\t(ii)\tLet the total number of man-hours they take, 187.5. to complete the work be 12x hours, where x is the number of days for which they work \t\t(iii)\tNow find the ratio of the efficiencies of P, Q together. and R. \t\t(iii)\tUse unitary method to equate the sum of their \t\t(iv)\tThen find the ratio of the time taken by P, Q individual work done per day to the work and R. done by both of them per day and proceed. \t\t(iv)\tNow, find the time taken by P, Q and R to \t32.\t (i)\tTank was filled in 8 hours P was opened all the complete the work. time. 3\t 5.\t (i)\tFrame the equations as follows: 1 \t\t(ii)\tTap P is opened for 8 hours. Let the tap Q be \t\t \t4m + 8w + 4 machine = 5 and 4m + 1w + 2 opened for x hours 1 \t\t(iii)\t182 + x = 1. machine = 10 . 18 \t\t(iv)\tRequired time = 7 am + x. \t\t(ii)\tSince the work done by a man in one day is \t33.\t (i)\tFind the capacity of Anand and proceed. known, work done by a women can be found. \t\t(ii)\tAnand can complete the work in (5 \u00d7 4) days. 3\t 6.\t Remaining work after 3 minutes is 7 . 10 \t37.\t (i)\tLet the efficiencies of a man, a woman and a \t\t(iii)\tRemaining work is four-fifth which is to be completed by both Anand and Bhargav. machine be x, y and z. \t34.\t (i)\tLet the amount of work done by R in a day be \t \t \t\u21d2 2x = 3y = 4z = k say. x units. \t\t(iii)\tFind x, y, z in terms of k.","Time and Work 22.25 \t\t(iv)\tThe ratio of shares of men, women and \t\t(iii)\tNow find the ratio of efficiencies of Anand, Raju, Suresh and Venkat and then divide 392 machines = 3 \uf8eb k\uf8f6 : 4 \uf8eb k \uf8f6 : 5 \uf8eb k \uf8f6 . in the same ratio. \uf8ec\uf8ed 2\uf8f7\uf8f8 \uf8ed\uf8ec 3 \uf8f7\uf8f8 \uf8ec\uf8ed 4 \uf8f8\uf8f7 3\t 8.\t Take filling work as positive and emptying work as \t\t(iv)\tNow, find the number of pieces produced by Raju in 8 hours, by using the number of pieces negative. produced by Raju in 6 hours 3\t 9.\t (i)\tQ and R take 9 days and 36 days respectively \t44.\t Let the work done on the first day be x. to complete a piece of work. \t\t(ii)\tLet P take x days, Q take 3x days, R take 12x \t\tThen the work done on the third day = 3 \u00d7 3 \u00d7 x days and S take 24x days. 4 4 which is equal to 36 units. \t\t(iii)\tFind the part of the work done by each person, per day. 4\t 5.\t B can do the work in 12 days. \t\t(iv)\tThen check from the options. \t46.\t Let the required number of hours per day be h. 4\t 0.\t (i)\tOn the first day 25 units of work is done. On \t\tLet the work done by each man be 1 unit\/hr. the second day 26 units, third day 27 units the work is done in this way. \t\tTime for which 27 men worked in the first four days = (5)(4) hours = 20 hours. \t\t(ii)\tLet 25 + 26 + 27 + \u2026 upto x terms = 330. \t\tWork completed in the first 4 days = (27)(1)(20) \t\t(iii)\tFind x. units = 540 units. \t41.\t (i)\tRemaining work = 1 \u2013 (P + Q + R)\u2019s two day\u2019s \t\tRemaining time = (20 \u2013 4)(h) hours = 16h hours work \u2013 (P + R)\u2019s one day work. \t\tWork completed in the remaining time = (27 \u2013 12) \t\t(ii)\tLet p, q and r be the number of days taken by (1)(16h) units = 240h units P, Q and R respectively. \t\tTotal time taken = (5)(20) hours = 100 hours Hints and Explanation \t\t(iii)\t 1 + 1 + 1 = 1 \b(1) \t\tTotal work = (27)(1)(100) units = 2700 units p q r 4 \t\t2700 = 540 + 240h \t\t\t 1 + 1 = 1 \b(2) \t\th = 9. 45 p r 6 5 4\t 7.\t 1 man can load = 9 boxes in 45 minutes. \t\t\t 3 + 2 + 11 = 1 \b(3) \t\tSo, 8 men can load 8 \u00d7 9 = 72 boxes in 45 minutes. p q r \t \t \u2234 They can load completely 7 trucks in 45 \t\t(iv)\tSolve the above equations to find P. minutes. \t42.\t (i)\tTap A is opened for 6 hours and Tap B for \t48.\t Let the required time be t days. 3 hours. \t\tPart of the job that five men can complete each \t\t(ii)\tLet C be opened for x hours . day = part of the job that ten women can complete 6 3 x 1 \t\t(iii)\tSolve 6 + 9 \u2212 7.5 = 1, for x. each day = 20 . \t43.\t (i)\tThe ratio of efficiency of Anand, Raju, Suresh \t\tPart of the job that each man can complete each and Venkat is 1 : 3 : 4 : 6. 1 \t\t(ii)\tLet the efficiency of Suresh be x. 2=50 1 100 \t\t \t\u2234 Efficiency of Anand = x . da=y . 4 \t\t \tEfficiency of Venkat = 3x . \t\tPart of the job that each woman can complete 2 1 \t\t \tEfficiency of Raju = 3x . each da=y 12=00 1 . 4 200","22.26 Chapter 22 \t\tPart of the job that four men and four women can \t49.\t A\u2019s 10 days wor=k 10 5 1=8 9 complete each day \t\t 4 \uf8eb 1 \uf8f6 + 4 \uf8eb 1\uf8f6 = 1 + 1 = 3 . \t\tA completed more than half the work. = \uf8ec\uf8ed 100 \uf8f7\uf8f8 \uf8ed\uf8ec 200 \uf8f8\uf8f7 25 50 50 \t\tHence A gets more share. \t\tTime taken by them to complete the job = 5=30 days 16 2 days. 3 Level 3 \t50.\t (i)\tWork done in the first three days is xx 1 + 2 + 3 and from the 4th day onwards \t\t(iii)\t 2 + 2 = 1. \b(2) 19 19 19 a 16 the work done is 4 . \t\t(iv)\tSimplify the Eq. (2) and assume the value of x 19 by using Eq. (1). \t\t(ii)\tPart of the work done in first three days \t54.\t (i)\tTime taken by X to fill the tank is 12 hours. = 1 + 2 + 3 = 6 . \t\t \tIf Y takes x hours to fill the tank, then X takes 19 19 19 19 2x hours to empty the full tank. \t\t \t\u2234 Remaining work = 13 . \t\t(ii)\tFirst 1 of the tank will be filled by Y and Z 19 4 \t\t(iii)\tLet time taken by the four together be x. in 3 hours. Hints and Explanation \t\t \t\u2234(x ) \uf8eb 4 \uf8f6 = 13 . \t\t(iii)\tRemaining \uf8eb 3\uf8f6 of the tank will be filled by \uf8ec\uf8ed 19 \uf8f7\uf8f8 19 \uf8ed\uf8ec 4\uf8f7\uf8f8 \t\t(iv)\tThe required time = (3 + x) days. X, Y and Z where X will be emptying. 5\t 1.\t (i)\tThe ratio of work done by P, Q and R is 7 : 18 \t55.\t Let the time in which X and Y can complete the : 25. job be x days and y days respectively. \t\t(ii)\tLet the efficiencies of P, Q and R be 2x, 3x \t\tx1 = 4 \uf8eb 1\uf8f6 \b(1) and 5x. \uf8ed\uf8ec y \uf8f7\uf8f8 \t\t(iii)\tUse, (14 \u00d7 2x) + (24 \u00d7 3x) + (20 \u00d7 5x) = 6000 \t\ty = x + 60. \b(2) and find x. \t\tFrom Eq. (1), we get \t\t(iv)\tNow, find (9 \u00d7 2x) + (14 \u00d7 3x) + (8 \u00d7 5x). \t\ty = 4x. \t\tSubstituting this value in Eq. (2), we get 5\t 2.\t (i)\tFrame the equations and solve. 4x = x + 60 \t\t(ii)\tA or B or C can make 8 dosas in one \t\tx = 20 3 minute. y = 80. \t\t(iii)\tLet A alone work for x minutes, and B and C work for (20 \u2212 x) minutes each. \t\t(iv)\t 83 \u00d7 x + (20 \u2212 x) 8 + (20 \u2212 x) 8 = 80. \t\tThe time in which X and Y can complete the job 3 3 (in days) = xy = 16. \t53.\t (i)\tConsider Ganesh to be as efficient as Eswar x+y and proceed. 5\t 6.\t Let the work which each man can complete each \t\t(ii)\tLet a be the time taken by Ganesh to complete day be m units. Let the work which each women the work. \u21d2 12 \u2264 a \u2264 16.\b (1) and complete each day be w units.","Time and Work 22.27 \t\tWork which one man and 7 women can complete And from Eq. (2), we get each day = (m + 7w) units \t\ts = 1 m. \t \t \u2234 Job = (m + 7w)16 units = (19m + 10w)3 3 \t\t82w = 41m \u2234 5 m + 5 m + 1 m + m = 46.5 6 12 3 \t\t2w = m. 31 Required time = Job days \t\t 12 m = 46.5 6m + 6w m = 18. 16(2w + 7w ) \t\t = 6(2w ) + 6w days \t\tIn 9 hours Mahesh can produce 9\u2009m units, i.e., 162 units. = 8 days. \t59.\t Let us assume that each of A, B and C alone can do in x days. 5\t 7.\t Part of the job completed (by M) on the first day = 1 . \t\tA works for 5 days, B works for 10 days and C 18 works 15 days. \t\tPart of the job completed (by N) on the second \u2234 5 + 10 + 15 = 1 \t\t x x x day = 1 . 20 30 x =1\u21d2 x = 30. \t\tPart of the job completed on the first two days = 1 + 1 = 19 . \t60.\t Let the areas that each man and each woman can 18 20 180 level (in sq. m.) be m\/day and w\/day respectively. \t\tPart of the job completed on the first 18 days \t \t\tArea that 18 men and 36 women can level each day = (18m + 36w) sq. m. = 18 \uf8eb 19 \uf8f6 = 19 . Hints and Explanation 2 \uf8ec\uf8ed 180\uf8f8\uf8f7 20 \t \t \u2234 6(18m + 36w) = 810 \t\tRemaining part = 1 . \t\t18m + 36w = 135. 20 \t\tGiven: m = 3 , i.e., m = 3w w 1 \t \t M work on the 19th day. He can complete the \t \t \u2234 18(3w) + 36w = 135 1 \t\t90w = 135 remaining part in 20 days = 9 days. \t\tw = 3 1 10 2 18 \t\tTotal time taken = 18 9 days. \t\t\u2234 m = 9 . 10 2 5\t 8.\t Let the number of units which Ganesh, Harish, \t\tLet the required number of days be d. Suresh and Mahesh can produce be g\/hr, h\/hr, s\/hr and m\/hr respectively. \t\td(22m +14w) = 1200 \t\t12(g + h + s + m) = 558 \t\td \uf8eb 22 \uf8eb 9 \uf8f6 + 14 \uf8eb 3 \uf8f6 \uf8f6 = 1200 \uf8ec \uf8ed\uf8ec 2 \uf8f8\uf8f7 \uf8ec\uf8ed 2 \uf8f8\uf8f7 \uf8f7 \uf8ed \uf8f8 \t\tg + h + s + m = 46.5 \u21d2 120d = 1200 \u21d2 d = 10. \t\t=g 2=h 5 m \b (1) \t61.\t On the mth day, (15 + m \u2013 1) workers would work. 6 (2) \t\tm = 3s.\b \t\tOn the first day, 15 workers would work. \t\tFrom Eq. (1), we get \t\tOn the second day, 16 workers would work and so on. \t\th 5 m. = 12 \t\tLet the time taken to complete the job be N days.","22.28 Chapter 22 N \t \t = (9w + 6c)(10) units = (m + w)(48) units Job = \u2211 (15 + m \u2212 1)(1) = 220 m=1 \t\t(2m + 3w + 4c)(15) = (9w + 6c)(10) \t\t N \t\t30m + 45w + 60c = 90w + 60c \u2211 (14 + m) = 220. \t\t30m = 45w m=1 \t\tm = 3 w. \t\t15 + 16 + 17 + \u2026 + (14 + N) = 220. 2 \t\tExpressing the RHS as a sum of consecutive natu- \t\t\u2234 Job = \uf8eb 3 w + w \uf8f6 (48) units ral numbers starting from 15, we have 15 + 16 + \uf8ed\uf8ec 2 \uf8f7\uf8f8 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25. = 120w units. \t \t \u2234 14 + N = 25 \t\tTime in which a man can complete it \t \t \u2234 N = 11. 6\t 2.\t Amar worked for 6 days. = 1=3220ww days 80 days. \t\tBhavan worked for (t \u2013 15) days \t\tChetan worked for t days, \t65.\t Time in which Mohan can complete the job = (8)(9) hours = 72 hours. \uf8eb 1 \uf8f6 15) \uf8ed\uf8ec\uf8eb 1 \uf8f6 \uf8eb 1 \uf8f6 Job = 6 \uf8ec\uf8ed 24 \uf8f8\uf8f7 + (t \u2212 36 \uf8f8\uf8f7 + t \uf8ed\uf8ec 48 \uf8f8\uf8f7 = 1 \t\tTime in which Sohan can complete it = (9)(10) hours = 90 hours. 1 \uf8eb 1 1 \uf8f6 5 \t\t 4 + t \uf8ec\uf8ed 36 + 48 \uf8f8\uf8f7 \u2212 12 =1 \t\tTime in which Mohan and Sohan can complete it 7t = 7 \t\t= (72)(90) hours = 40 hours. 144 6 72 + 90 t = 24. \t\tNumber of days in which they can complete it Hints and Explanation \t63.\t Each man can complete 1 of the job\/day. \t\t40 = 40 days = 5 days. 35 8 6\t 6.\t One of Kiran and Pavan would work on the first \t\tPart of the job completed in the first 5 days. day and the other person would work on the 1 2 3 4 5 15 3 . second day. Irrespective of who works on the first 35 35 35 35 35 35 7 \t\t= + + + + = = day, part of the job completed in the first two days \t\tRemaining part = 4 = 1 + 1 = 9 . 7 40 50 200 \t\tThis will be completed by all the men working \t\tPart of the job completed in the first 44 days together. = 44 \uf8eb 9\uf8f6 = 198 = 99 2 \uf8ec\uf8ed 200 \uf8f7\uf8f8 200 100 \t\tTime taken to complete it 1 4 \t\tRemaining part = 100 . \t\t= 7 days = 4 days. \t\tThis will be completed in the minimum possible time if the person with a higher efficiency between 5 \uf8eb 1\uf8f6 the two completed. \uf8ed\uf8ec 35\uf8f7\uf8f8 \t\tTotal time taken = 9 days. \t \t \u2234 Total time taken will be minimum if Kiran completed. 6\t 4.\t Let the work which can be completed each day by each man, each woman and each child be m units, \t\tMinimum possible total time = 44 days + w units, and c units respectively. 1 \t\tWork which two men, three women and four children can complete = (2m + 3w + 4c) units 100 days = 44 2 days. 1 5 \t \t \u2234 Job = (2m + 3w + 4c)(15) units 40","Time and Work 22.29 \t67.\t Each of A and B can fill the bottom one-third of 6\t 9.\t Part of the tank which X and Y can fill in one 1 the tank in 3 (9) hours = 3 hours. hour = 1 + 1 = 7 . 18 24 72 \t\tTime in which it will be filled = (3)(3) hours = 3 \t\tPart of the tank that Z can empty in one hour 3+3 2 1 8 1 = 9= 72 . 1 2 hours = hours. \t\tEmptying rate of Z > filling rate of X and Y. \t\tPart of the top two-third of the tank which A, B \t \t \u2234 The tank will be emptied. and C can fill each hour \t\tPart of it emptied each hour 8 7 1 . 1 \uf8eb 1 1 1 \uf8f6 1 1 1 5 = 72 \u2212 72 = 72 2 \uf8ed\uf8ec 9 9 12 \uf8f8\uf8f7 6 6 8 24 . \t\t= + \u2212 = + \u2212 = 1 3 \t\tTime taken to empty 2 of the tank \t \t \u2234 Time in which it will be filled = 24 hours. 1 5 2 hours \t\tTotal time in which the tank will be filled \t\t= 1 3 24 = 2 + 5 = 6.3 hours. 72 6\t 8.\t Parts of the job completed by P and Q each day are = 36 hours. 1 1 \t70.\t Let the time taken to complete the job be x days. 60 90 and respectively. \t\tParts of the job complete by P, Q and R each day \t\tParts of the job completed by P and Q are are 1 , 1 and 1 respectively. 6 9 12 \t\t20 \uf8eb 1\uf8f6 1 and 20 \uf8eb 1\uf8f6 2 respectively. Hints and Explanation \uf8ed\uf8ec 60 \uf8f8\uf8f7 =3 \uf8ed\uf8ec 90 \uf8f8\uf8f7 =9 \t\tParts of the job completed by P, Q and R are \t\tPart of the job completed by x \uf8eb 1 \uf8f6 , x \uf8eb 1 \uf8f6 and x \uf8eb 1 \uf8f6 respectively. \uf8ec\uf8ed 6 \uf8f7\uf8f8 \uf8ed\uf8ec 9 \uf8f7\uf8f8 \uf8ec\uf8ed 12 \uf8f7\uf8f8 \uf8eb 1 2 \uf8f6 4 \t\tR = 1 \u2212 \uf8ed\uf8ec 3 + 9 \uf8f8\uf8f7 = 9 . \t\tRatio of the parts of the job completed by P, Q and \t\tRatio of the parts of the job completed by P, Q x6=: x9 : 1x2 1 1 1 =and R 31=: 92 : 49 3 : 2 : 4. =\t\tR 6 : 9 : 12 = 6 :4 : 3. \t \t \u2234 The ratio of the share of P, Q and R = 3 : 2 : 4. \t \t \u2234 Ratio of the shares of P, Q and R = 6 : 4 : 3. \t \t \u2234 R\u2019s share = 3 + 4 + 4 \u00d7 `3600 \t \t \u2234 P\u2019s share = 6 6 + 3 (`2600) 2 +4 \t \t = `1600. \t \t = `1200.","This page is intentionally left blank"]
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