Maths new edition

["16.18 Chapter 16 Level 2 \t31.\t If sin\u2009\u03b1 + cos\u2009\u03b1 = n, then sin6\u03b1 + cos6\u03b1 in terms of \t\t(a) sin \uf8eb x \uf8f6 + cos \uf8eb x \uf8f6 n is ______. \uf8ed\uf8ec 8 \uf8f7\uf8f8 \uf8ec\uf8ed 8 \uf8f8\uf8f7 4 + 3(n2 \u2212 1) \t\t(a) 4 + 3(n \u2212 1)2\t(b) 4 x\uf8f6 x\uf8f6 \t\t(b) sin \uf8eb 16\uf8f7\uf8f8 + cos \uf8eb 16\uf8f7\uf8f8 4 \u2212 3(n2 \u2212 1)2 \uf8ed\uf8ec \uf8ec\uf8ed \t\t(c) 4 \t (d) None of these \uf8eb x \uf8f6 \uf8eb x \uf8f6 sin 25\u00b0 cos 25\u00b0 \t\t(c) sin \uf8ec\uf8ed 4 \uf8f7\uf8f8 + cos \uf8ec\uf8ed 4 \uf8f7\uf8f8 cos 35\u00b0 sin 35\u00b0 \t32.\t Find the value of \u2212 . \t\t(d) None of these \t\t(a) cosec 70\u00b0\t (b) sin 70\u00b0 \t40.\t sin4\u03b8 + cos4\u03b8 in terms of sin\u2009\u03b8 is ______. \t\t(c) \u2013sin 70\u00b0\t\t (d) \u2013cosec 70\u00b0 \t\t(a) 2sin4\u03b8 \u2212 2sin2\u03b8 \u2212 1 \t33.\t The value of 3 tan 30\u00b0 \u2212 tan3 30\u00b0 is ______. \t\t(b) 2sin4\u03b8 \u2212 2sin2\u03b8 + 1 1 \u2212 3 tan2 30\u00b0 \t\t(c) 2sin4\u03b8 + 2sin2\u03b8 \u2212 1 \t\t(a) tan 90\u00b0\t\t (b) tan 60\u00b0 \t\t(d) 2sin4\u03b8 \u2212 2sin2\u03b8 \t\t(c) tan 45\u00b0\t\t (d) tan 30\u00b0 3 3\t 4.\t If cot4x \u2212 cot2x = 1, then the value of cos4x + \t41.\t If tan(A \u2212 B) = 1 and sin(A + B) = 2 , then cos2x is ______. find B. \t\t(a) \u22121\t\t (b) 0 \t\t(a) 42 1\u00b0 \t\u22c5 \t (b) 7 1\u00b0 2 2 \u22c5 \t\t(c) 2\t\t (d) 1 \t35.\t If cos( A \u2212 B) = 8 , then tanA \u00b7 tan\u2009B is ______. \t\t(c) 15 1\u00b0 \u22c5\t\t (d) 60\u00b0 cos( A + B) 3 2 \t\t(a) 5 \t\t (b) 7 \t42.\t If sin \u03b2 + cos \u03b2 = 5 , then find the value of sin\u2009\u03b2 \u22c5 11 13 4 PRACTICE QUESTIONS \t\t(c) 8 \t\t (d) 11 cos\u2009\u03b2. 5 5 \t\t(a) 1 \t\t (b) 9 4 32 \t36.\t If A + B + C = 45\u00b0, then the value of 5 11 \u2211 (tan A + tan A tan B) is ______. \t\t(c) 16 \t\t (d) 32 \t\t(a) 1 \u2212 \u03c0\u2009tan\u2009A\t (b) 1 \t43.\t If sin2\u2009\u03b1 + sin\u2009\u03b1 = 1, then the value of cos4\u03b1 + cos2\u2009\u03b1 is ______. \t\t(c) 1 + \u03c0\u2009tan\u2009A\t (d) 1 + \u03a3tan\u2009A 3\t 7.\t If cot\u2009\u03b8 + tan\u2009\u03b8 = 2, then the value of tan2\u03b8 \u2212 cot2\u03b8 \t\t(a) 0\t\t (b) \u22121 is ______. \t\t(c) 1\t\t (d) 2 \t\t(a) 1\t\t (b) 0 4\t 4.\t If tan\u2009P + cot\u2009P = 2, then the value of tannP + cotnP is ______. \t\t(c) \u22121\t\t (d) 2 3\t 8.\t The value of cot\u20095\u00b0 \u22c5 cot\u200915\u00b0 \u22c5 cot\u200925\u00b0 \u22c5 cot\u200935\u00b0 \u22c5 \t\t(a) 2\t\t (b) 2n cot\u200945\u00b0 \u22c5 cot\u200955\u00b0 \u22c5 cot\u200965\u00b0 \u22c5 cot\u200975\u00b0 \u22c5 cot\u200985\u00b0 is ______. \t\t(c) 2n\u22121\t\t (d) 2n+1 \t\t(a) 0\t\t (b) \u22121 \t45.\t The value of 3 tan10\u00b0 + 3 tan\u200920\u00b0 + tan\u200910\u00b0 \u22c5 tan\u200920\u00b0 is ______. \t\t(c) \u22122\t\t (d) 1 3\t 9.\t The simplified form of 1+ sin \uf8eb x\uf8f6 is ______. \t\t(a) \u22121\t\t (b) 0 \uf8ed\uf8ec 8 \uf8f7\uf8f8 \t\t(c) 1\t\t (d) 2","Trigonometry 16.19 \t46.\t If tan (A + B) = 1 and (A \u2212 B) = 1 , then find A \t\t(C) \u0007cos (A \u2212 B) = 1 \u21d2 cos (A \u2212 B) = cos 60\u00b0 and and B. 2 2 \t\tThe following are the steps involved in solving the sin (A + B) = 3 \u21d2 sin( A + B) = sin 60\u00b0. above problem. Arrange them in sequential order. 2 \t\t(D) A + B = 60\u00b0 and A \u2212 B = 60\u00b0. \t\t(A) t\u0007 an(A + B) = 1 \u21d2 tan(A + B) = tan\u200945\u00b0 and \t\t(a) DCAB\t\t (b) CADB sin(A \u2212 B) = 1 \u21d2 sin(A \u2212 B) = sin 45\u00b0. 2 \t\t(c) DCBA\t\t (d) CDAB \t\t(B) 2A = 90\u00b0 \u21d2 A = 45\u00b0. \t48.\t If sin\u2009\u03b1 + sin\u2009\u03b2 + sin\u2009\u03b3 \u2009= 3, then sin3\u2009\u03b1 + sin3\u2009\u03b2 + sin3\u2009\u03b3 = _______. \t\t(C) A + B = 45\u00b0 and A \u2212 B = 45\u00b0. \t\t(a) 0\t\t (b) 2 \t\t(D) \u2234 A = 45\u00b0 and B = 0\u00b0. \t\t(c) 3\t\t (d) 1 \t\t(a) DBCA\t\t (b) CABD \t49.\t sec4\u2009\u03b8 \u2212 sec2\u2009\u03b8 = _______. \t\t(c) ACDB\t\t (d) ACBD \t\t(a) tan2\u2009\u03b8 sec2\u2009\u03b8\t (b) tan2 \u03b8 sec2 \u03b8 4\t 7.\t If cos\u2009(A B)\u2009\u2009 = 1 and sin(A + B) = 3 , then \u2212 2 2 cot2 \u03b8 \t\t(c) cosec2\u2009\u03b8 cot2\u2009\u03b8\t (d) cos ec2 \u03b8 find A and B. \t\tThe following are the steps involved in solving the \t50.\t sin\u03b8 + cos\u03b8 = 2, then sin16\u2009\u03b8 = _______. following problem. Arrange them in sequential order. \t\t(a) cos16 \u03b8 \t\t (b) sec16 \u03b8 216 28 \t\t(A) 2A = 120\u00b0 \u21d2 A = 60\u00b0. 1 1 \t\t(B) \u2234A = 60\u00b0, B = 0\u00b0. \t\t(c) 2 sec16 \u03b8 \t(d) 216 cos16 \u03b8 Level 3 PRACTICE QUESTIONS \t51.\t If sin(x \u2212 y) = 3 , then tan\u2009x \u00b7 cot\u2009y is _______. \t54.\t If sin\u2009\u03b1 \u2212 cos\u2009\u03b1 = m, then the value of sin6\u03b1 + cos6\u03b1 sin(x + y) 5 in terms of m is _______. \t\t(a) 1\t\t (b) 2 3 4 4 3 \t\t(c) 3\t\t (d) 4 \t\t(a) 1+ (1 + m2 )2 \t(b) 1\u2212 (m2 \u2212 1)2 \t52.\t 16 sin4 \u03b8 + cosec4\u03b8 + 8 \u2212 4 = \t\t(c) 1\u2212 3 (1 \u2212 m2 )2 \t(d) 1\u2212 3 (1 + m2 )2 4 4 \t\t(a)\t2sin\u2009\u03b8 \u2013 cosec\u2009\u03b8 \t\t(b) 2sin\u2009\u03b8 + cosec\u2009\u03b8 5\t 5.\t The value of 8 sec4\u03b8 \u2212 8 tan4\u03b8 \u2212 2 cos6\u03b8 + 2 sin6\u03b8 \t\t(c) 2cosec\u2009\u03b8 + cos\u2009\u03b8 4 + 8 tan2\u03b8 1\u2212 3 sin2\u03b8 cos2\u03b8 \t\t(d) 2cosec\u2009\u03b8 + sin\u2009\u03b8 is _______. \t53.\t If sin\u2009\u03b8 and cos\u2009\u03b8 are the roots of the quadratic \t\t(a) 0\t\t (b) 1 equation px2 + qx + r = 0 (p \u2260 0), then which of the following relation holds good? \t\t(c) \u22121\t\t (d) 3 \t\t(a) q2 \u2212 p2 = 2pr \t56.\t If 1+ tan \u03b8 = 3, then find the value of \u03b8. \t\t(b) p2 \u2212 q2 = 2pr 1\u2212 tan \u03b8 \t\t(c) p2 + q2 + 2pr = 0 \t\t(d) (p \u2212 q)2 = 2pr \t\t(a) 30\u00b0\t\t (b) 25\u00b0 \t\t(c) 15\u00b0\t\t (d) 45\u00b0","16.20 Chapter 16 \t57.\t If A \u00d7 B = 1, A + B = cosec\u2009\u03b8 \u22c5 sec\u2009\u03b8 then A can \t\t(a) 1 \t\t (b) 3 be ______. B 3 \t\t(a) tan2\u2009\u03b8\t\t (b) sec2\u2009\u03b8 \t\t(c) 1\t\t (d) \u221e \t\t (c) sin2\u2009\u03b8 cos2\u2009\u03b8\t (d) cosec2\u2009\u03b8\u2009sec2\u2009\u03b8 \t63.\t If sin\u2009\u03b1 + sin\u2009\u03b2 = 2, then find the value of cos2\u03b1 + cos2\u03b2. \t58.\t If 7sin2\u2009\u03b8 + 3cos2\u2009\u03b8 = 4, then find tan\u2009\u03b8. \t\t(a) 1 \t\t (b) 2 \t\t(a) 0\t\t (b) 1 33 \t\t(c) 2\t\t (d) 3 \t\t(c) 3 \t\t (d) 1 \t64.\t If x = a2cos3\u2009\u03b8 and y = b2sin3\u2009\u03b8, then \t59.\t If sin(A + B) = 3 +1 and sec\u2009A = 2, then the \t\t(a) x2 + y2 =1 22 a b value of B in circular measure is ______. \t\t(b) \uf8eb x \uf8f61\/3 + \uf8eby \uf8f61\/3 =1 \uf8ed\uf8ec a2 \uf8f8\uf8f7 \uf8ec\uf8ed b2 \uf8f8\uf8f7 \t\t(a) \u03c0 \t \t(b) 3\u03c0 12 \u03c4 5 \u03c4 \t\t(c) \uf8eb x2 \uf8f62\/3 + \uf8eb y2 \uf8f62\/3 =1 7\u03c0 5\u03c0 \uf8ec \uf8f7 \uf8ec \uf8f7 \t\t(c) 5 \u03c4 \t\t (d) 12 \u03c4 \uf8ed a2 \uf8f8 \uf8ed b2 \uf8f8 \t60.\t If tan\u2009\u03b8 \u2212 cot\u2009\u03b8 = 7, then the value of tan3\u2009\u03b8 \u2212 cot3\u2009\u03b8 \t\t(d) \uf8eb x \uf8f62\/3 + \uf8eby \uf8f62\/3 =1 is \uf8ed\uf8ec a2 \uf8f8\uf8f7 \uf8ec\uf8ed b2 \uf8f7\uf8f8 \t\t(a) 250\t\t (b) 354 \t65.\t If cos2\u2009\u03b8 + 2sin2\u2009\u03b8 + 3cos2\u2009\u03b8 + 4sin2\u2009\u03b8 + \u2026 \t\t(c) 343\t\t (d) 364 (200 terms) = 10025, where \u03b8 is acute, then the value of sin\u2009\u03b8 \u2212 cos\u2009\u03b8 is \t61.\t If xn = am cos4\u2009\u03b8 and yn = bm sin4\u2009\u03b8, then 1\u2212 3 xn\/2 yn\/2 xn yn \t\t(a) 2 \t\t(a) am\/2 + bm\/2 = 1 \t(b) am + bm =1 PRACTICE QUESTIONS xn\/2 am\/2 \t\t(b) 1+ 3 yn\/2 bm\/2 2 \t\t(c) + = 1 \t(d) None of these \t62.\t If sin2\u2009\u03b8 + 2cos2\u2009\u03b8 + 3sin2\u2009\u03b8 + 4cos2\u2009\u03b8 + \u2026 + \t\t(c) 3 \u22121 40 terms = 405 where \u03b8 is acute, then find the 2 value of tan\u2009\u03b8. \t\t(d) 0","Trigonometry 16.21 TEST YOUR CONCEPTS Very Short Answer Type Questions \t1.\t 4\u03c0 \u03c4 1\t 1.\t 3 \u2212 1 5 1 \t2.\t 3 \t12.\t 4 4 \t13.\t 2 \t3.\t 120\u00b0 \t14.\t 3 2 \t4.\t 0 \t5.\t 58\u00b0 \t15.\t 2cos\u2009A cos\u2009B \t6.\t 1 1\t 6.\t 1(B and C are complementary) 2 1\t 7.\t \u03c0 1 12 \u03c4 \t7.\t x cosC 24 1 \t18.\t = 25 2 \t8.\t \t19.\t A + B = 90\u00b0 \t9.\t 2 \t20.\t 1(A = 45\u00b0, C = 45\u00b0) 1\t 0.\t 45\u00b0 Shot Answer Type Questions \t21.\t 3 \t33.\t 4 3 cm 32 3 +1 \t22.\t \u221217 3\t 4.\t 3 \u22121 61 \t35.\t \u00b12 3 +1 \t23.\t 22 \t36.\t x2 + y2 = a2 + b2 2\t 4.\t 8 1 \t37.\t 63 3 65 \t25.\t 40 g \t38.\t 1 ANSWER KEYS 3 1 + cot2 \u03b8 \t26.\t 4 \t39.\t 24 3 25 \t27.\t sec2\u2009a + tan2\u2009a \t40.\t 1 \u2212X \t28.\t 60\u00b0, \u03c0 3 \t41.\t 132 cm 300 g , 3\u03c0 c \t42.\t 1 or \u22123 2 3 \t29.\t \u03c4 \t30.\t 2 \t43.\t 1 \t31.\t 25 4\t 4.\t A = 52 1 \u00b0 \u22c5 and B = 7 1 \u00b0 \u22c5 5 2 2 \t32.\t 80\u03c0\u2009c 4\t 5.\t l\u20092 \u2212 m2 = 2nl","16.22 Chapter 16 Essay Type Questions \t49.\t 18 3 \t50.\t cot r \t47.\t 6 4\t 8.\t (x \u2212 a)2 + (y \u2212 b)2 = r2 CONCEPT APPLICATION Level 1 \t 1.\u2002 (d) \t 2.\u2002(a)\t 3.\u2002(d)\t 4.\u2002(d)\t 5.\u2002(a)\t 6.\u2002(b)\t 7.\u2002(a)\t 8.\u2002(c)\t 9.\u2002(a)\t 10.\u2002(c) \t11.\u2002(d)\t 12.\u2002(b)\t 13.\u2002(b)\t 14.\u2002(a)\t 15.\u2002(d)\t 16.\u2002(d)\t 17.\u2002(b)\t 18.\u2002(d)\t 19.\u2002(d)\t 20.\u2002(c) \t21.\u2002(d)\t 22.\u2002(c)\t 23.\u2002(b)\t 24.\u2002(d)\t 25.\u2002(c)\t 26.\u2002(d)\t 27.\u2002(c)\t 28.\u2002(b)\t 29.\u2002(b)\t 30.\u2002(d) Level 2 33\u2002(a)\t 34.\u2002(d)\t 35.\u2002(a)\t 36.\u2002(c)\t 37.\u2002(b)\t 38.\u2002(d)\t 39.\u2002(b)\t 40.\u2002(b) 43.\u2002(c)\t 44.\u2002(a)\t 45.\u2002(c)\t 46.\u2002(d)\t 47.\u2002(d)\t 48.\u2002(c)\t 49.\u2002(a)\t 50.\u2002(d) \t31.\u2002(c)\t 32. (d)\t \t41.\u2002(b)\t 42.\u2002(b)\t Level 3 53.\u2002(a)\t 54.\u2002(c)\t 55.\u2002(a)\t 56.\u2002(c)\t 57.\u2002(a)\t 58.\u2002(a)\t 59.\u2002(a)\t 60.\u2002(d) 63.\u2002(a)\t 64.\u2002(d)\t 65.\u2002(a) \t51.\u2002(d)\t 52.\u2002(c)\t \t61.\u2002(a)\t 62.\u2002(b)\t ANSWER KEYS","Trigonometry 16.23 CONCEPT APPLICATION Level 1 \t1.\t (i)\t\u0007The minutes hand covers an angle of 6\u00b0 per \t16.\t Apply cos\u03b8 = Side adjacent to \u03b8 , minute. Hypotenuse \t\t(ii)\tUse l = r \u00d7 \u03b8. tan \u03b8 = Side opposite to \u03b8 . \t\t Side adjacent to \u03b8 \t2.\t Use tan\u2009\u03b8 \u00b7 tan(90 \u2212 \u03b8) = 1. \t3.\t Use sec2\u2009\u03b8 \u2212 tan2\u2009\u03b8 = 1. \t17.\t \u2009\u2009(i) Minutes hand moves 6\u00b0 in one minute. \t4.\t Take the values of trigonometric ratios from the \t\t(ii) Use l = r \u00d7 \u03b8. table. 1\t 8.\t Use sin\u20092\u03b1 = 2sin\u2009\u03b1\u2009cos\u2009\u03b1. \t5.\t Use (a + b)(a \u2212 b) = a2 \u2212 b2 and cos2\u2009\u03b8 + sin2\u2009\u03b8 = 1. 1\t 9.\t In triangle ABC, A + B = 180 \u2212 C . 2 2 \t20.\t Apply a2 \u2212 b2 = (a + b)(a \u2212 b). \t6.\t Use, 1 revolution = 2\u03c0. \t7.\t Find sin\u2009A, cos\u2009A using triangle ABC. \t22.\t Apply (a + b)2 + (a \u2212 b)2 = 2(a2 + b2) and sin2\u2009\u03b8 + tan\u03b1 + tan \u03b2 cos2\u2009\u03b8 = 1. 1 \u2212 tan\u03b1 tan \u03b2 \t8.\t Use the identity tan(\u03b1 + \u03b2)= . 2\t 3.\t Use tan\u200945\u00b0 = 1 and sin 60\u00b0 = 3 . 2 \t24.\t Use (a + b)(a \u2212 b) = a2 \u2212 b2 and solve. \t9.\t Apply tan(A + B) = tan A + tan B . 1 \u2212 tan A tan B 1 \u2212 tan2 \u03b8 \t25.\t Use cos 2\u03b8 = 1 + tan2 \u03b8 . \u03c0. \t10.\t Find the value of A and then multiply it by 180 \u03c4 \t26.\t Use a2 + b2 = (a + b)2 \u2212 2ab. Hints and Explanation 1\t 1.\t Replace \u03c0\u2009c by 180\u00b0. \t27.\t 1 + sin\u20092\u03b8 = (sin\u2009\u03b8 + cos\u2009\u03b8)2, when \u03b8 \u2208 \uf8ee\uf8f0\uf8ef0, \u03c0 \uf8f9 . 4 \uf8fa\uf8fb 1\t 2.\t Use cos2\u2009\u03b8 + sin2\u2009\u03b8 = 1. \t28.\t (i)\tsin2A = sin2(90 \u2212 B). If A and B complemen- \t13.\t Observe the values of trigonometric ratios from tary angles. table. \t\t(ii)\tIf A + B = 90\u00b0, then sin\u2009A = cos\u2009B and tan\u2009B = \t14.\t Use l = r \u00d7 \u03b8, where \u03b8 is in radians. cot\u2009A. 1\t 5.\t Use the identity a2 + b2 = (a + b)2 \u2212 2ab. 2\t 9.\t Use trigonometric ratios values from table. 3\t 0.\t Squaring both sides of given equation. Level 2 3\t 3.\t (i)\tUse tan 30\u00b0 = 1. \t31.\t (i)\tsin6\u03b1 + cos6\u03b1 = (sin2\u03b1)3 + (cos2\u03b1)3. Use the 3 formula a3 + b3 = (a + b)3 \u2212 3ab(a + b). \t\t(ii)\tSubstitute the value of tan\u200930\u00b0 and simplify. \t\t(ii)\tFind sin\u2009\u03b1 \u22c5 cos\u2009\u03b1 by substituting sin\u2009\u03b1 + cos\u2009\u03b1 \t\t(iii)\tThen check from the options. = n in the above equation. \t32.\t (i)\tUse cos\u2009A cos\u2009B \u2212 sin\u2009A sin\u2009B = cos(A + B) and 3\t 4.\t Use cosec2x = 1 + cot2x and sin2x + cos2x = 1. sin\u20092A = 2sin\u2009A cos\u2009A. 3\t 5.\t (i)\tUse componendo and dividendo theorem, i.e., \t\t(ii)\t Find the LCM of denominators and simplify. \t\t(iii)\tUse the formula cos(A + B) = cos\u2009A cos\u2009B \u2212 \t\t \t a = a + b . b a \u2212 b sin\u2009A sin\u2009B. \t\t(ii)\tUse the formula cos(A \u2212 B) and cos(A + B). \t\t(iii)\tTake cross multiplication and find tanA + tan\u2009B.","16.24 Chapter 16 \t36.\t Use tan(A + B) = tan(45\u00b0 \u2212 C) and proceed. \t\t(iv)\tSubstitute the above values in the given 3\t 7.\t (i)\tPut \u03b8 = 45\u00b0. expression. \t\t(ii)\tIf tan\u2009\u03b8 + cot\u2009\u03b8 = 2, then \u03b8 = 45\u00b0. 3\t 8.\t Use cot\u2009A \u00b7 cot(90 \u2212 A) = 1. 4\t 4.\t If x + 1 = 2, then xn + 1 = 2. x xn \t39.\t (i)\tApply 1 + sin 2A = sin A + cos A. 4\t 5.\t (i)\tUse tan(A + B) = tan A + tan B . 1 \u2212 tan A tan B x x\uf8f6 \t\t(ii)\tsin 8 = sin 2 \uf8eb 16\uf8f7\uf8f8 and sin\u20092\u03b8 = 2sin\u2009\u03b8 cos\u2009\u03b8. \t\t(ii)\tTake tan(10\u00b0 + 20\u00b0) = tan\u200930\u00b0, i.e., \uf8ed\uf8ec tan10\u00b0 + tan 20\u00b0 = 1 and simplify. \t\t(iii)\tUse the identity 1 = sin2\u03b8 + cos2\u03b8. 1 \u2212 tan10\u00b0 \u22c5 tan 20\u00b0 3 \t40.\t (i)\tUse (a + b)2 = a2 + b2 + 2ab and cos2\u03b8 = 4\t 6.\t ACBD is the required sequential order. 1 \u2212 sin2\u03b8. 4\t 7.\t CDAB is the required sequential order. \t\t(ii)\tTake cos\u20094\u03b8 as (1 \u2212 sin2\u03b8)2 and simplify. \t48.\t Given, sin\u2009\u03b1 + sin\u2009\u03b2 + sin\u2009\u03b3 \u2009= 3. (i)\tUse tan\u200945\u00b0 = 1 and sin 60\u00b0 = 3 . 4\t 1.\t 2 \t\tThis is possible only if sin \u03b1 = sin \u03b2 = sin\u2009\u03b3 = 1, i.e., if \u03b1 = \u03b2 = \u03b3 = 90\u00b0. \t\t(ii)\tIf tan(A \u2212 B) = 1, then A \u2212 B = 45\u00b0. \t\t(iii)\tIf sin(A + B) = 3 , then A + B = 60\u00b0. \t\t \u2234sin3\u03b1 + sin3\u03b2 + sin3\u03b3 = 13 + 13 + 13 = 3. 2 \t\t(iv)\tSubtract the above two equations and find B. 4\t 9.\t sec4\u2009\u03b8 \u2212 sec2\u2009\u03b8 = sec2\u2009\u03b8(sec2\u2009\u03b8 \u2212 1) = sec2\u2009\u03b8 tan2\u2009\u03b8. \t42.\t (i)\tBy squaring on both the sides of the given 5\t 0.\t sin\u03b8 + cos\u03b8 = 2 equation we can obtain. \t\tsin2\u03b8 + cos2\u03b8 + 2sin\u2009\u03b8 cos\u2009\u03b8 = 2 \t\t(ii)\tSquare on both sides of sin \u03b2 + cos \u03b2 = 5 . \t\t \u21d2 2sin\u2009\u03b8 cos\u2009\u03b8 = 1 4 Hints and Explanation \t43.\t (i)\tUse sin2x + cot2x = 1. \t\tsin\u2009\u03b8 cos\u2009\u03b8 = 1 2 \t\t(ii)\tcos4\u03b1 = (1 \u2212 sin2\u03b1)2. \t\tsin16 \u03b8 = 1 . \t\t(iii)\tcos2\u03b1 = (1 \u2212 sin2\u03b1). 216 cos16 \u03b8 Level 3 \t51.\t (i)\tApply componendo and dividendo rule, i.e., \t54.\t (i)\tUse the identity a3 + b3 = (a + b)3 = 3ab(a + b). \t\t(ii)\tFind the value of sin\u2009\u03b1 cos\u2009\u03b1 by squaring a = a + b . b a \u2212 b sin\u2009\u03b1 \u2212 cos\u2009\u03b1 = m. \t55.\t (i)\tPut \u03b8 = 0 and simplify. \t\t(ii)\tUse the formula sin(x \u2212 y) and sin(x + y). \t\t(ii)\tsec4\u03b8 \u2212 tan4\u03b8 = sec2\u03b8 + tan2\u03b8. \t\t(iii)\ta3 + b3 = (a + b)3 \u2212 3ab(a + b). \t\t(iii)\tAnd then apply cross multiplication. 5\t 2.\t Use a2 + b2 + 2ab = (a + b)2 and sin\u2009\u03b8 \u22c5 cosec\u2009\u03b8 = 1. \t53.\t (i)\tFor the equation ax2 + bx + c = 0, the sum of 1 + tan\u03b8 1 \u2212 tan\u03b8 roots is \u2212b , and product of the roots is c . \t56.\t = 3 a a \t\t(ii)\tSum of the roots, sin \u03b8 + cos\u03b8 = \u2212q . \t\t1t\u2212anta4n54+5 tan \u03b8 = 3 p \u22c5 tan\u03b8 \t\t(iii)\tProduct of the roots sin \u03b8 \u22c5 cos\u03b8 = r . \t\ttan(45\u00b0 + \u03b8) = tan 60\u00b0 p \t\t \u21d2 45\u00b0 + \u03b8 = 60\u00b0 \t\t(iv)\tEliminate \u03b8, by using the formula (a + b)2 = a2 + b2 + 2ab from the above equations. \t\t \u03b8 = 60\u00b0 \u2212 45\u00b0 = 15\u00b0.","Trigonometry 16.25 \t57.\t AB = 1\u21d2 A = 1 \t\ttan3\u2009\u03b8 \u2212 cot3\u2009\u03b8 = (tan\u2009\u03b8 \u2212 cot\u2009\u03b8)3 + 3tan\u2009\u03b8 cot\u2009\u03b8\u2009 B (tan\u2009\u03b8 \u2212 cot\u2009\u03b8) \t\tA + B = 1 1 = 1 \t\t = 73 + 3(7) = 343 + 21 = 364. sin \u03b8 cos\u03b8 sin\u03b8 cos\u03b8 \t61.\t xn = amcos4\u03b8, and yn = bm sin4\u03b8 \t\t= sin2 \u03b8 + cos2 \u03b8 \t\t\u21d2 cos4 \u03b8 = xn and sin4\u03b8 = yn sin\u03b8 cos\u03b8 am bm \t\tA + B = sin \u03b8 + cos\u03b8 \t\t\u21d2 cos2 \u03b8 = xn\/2 , sin2 \u03b8 = yn\/2 . cos\u03b8 sin \u03b8 am\/2 bm\/2 \t\tA + B = tan\u2009\u03b8 + cot\u2009\u03b8. \t\tBut, sin2\u2009\u03b8 + cos2\u2009\u03b8 = 1 \t\tSince, tan\u2009\u03b8 \u00d7 cot\u2009\u03b8 = 1 = AB. \t\t\u2234 xn\/2 + yn\/2 = 1. am\/2 bm\/2 \t\t \u2234 A = tan\u2009\u03b8, B = cot\u2009\u03b8. A = tan \u03b8 = tan \u03b8 \u22c5 tan\u03b8 = tan2 \u03b8 . \t62.\t Given, = cot \u03b8 B = tan \t\tB A \t\tsin2\u2009\u03b8 + 2cos2\u2009\u03b8 + 3sin2\u2009\u03b8 + \u2026 40 terms = 405 A cot\u03b8 , B \u03b8, = cot2 \u03b8. \t\t \u21d2 (sin2\u2009\u03b8 + 3sin2\u2009\u03b8 + \u2026 20 terms) + (2cos2\u2009\u03b8 + 4cos2\u2009\u03b8 + \u2026 20 terms) = 405 \t58.\t 3sin2\u03b8 + 4sin2\u03b8 + 3 cos2\u03b8 = 4 \t\t \u21d2 202sin2\u2009\u03b8 + (202 + 20) cos2\u2009\u03b8 = 405 \t\t3 + 4sin2\u03b8 = 4 \t\t \u21d2 400(sin2\u2009\u03b8 + cos2\u2009\u03b8) + 20 cos2\u2009\u03b8 = 405 \t\t4 sin2\u03b8 = 1 \t\tsin\u03b8 = 1 = 1 \t\t \u21d2 400 + 20cos2\u2009\u03b8 = 405 = 20cos2\u2009\u03b8 = 5 4 2 \t\t \u21d2 cos2\u2009\u03b8 = 1 Hints and Explanation \t\t \u03b8 = 30\u00b0. 4 \t\t\u2234tan\u03b8 = 1. \t\t \u21d2 cos\u2009\u03b8 = 1 ( \u03b8 is acute) 3 2 \t59.\t sin(A + B) = 3 +1 \t\t\u21d2 \u03b8 = 60\u00b0. 22 \t\t\u2234 tan 60\u00b0 = 3. \t\tsin(A + B) = sin\u200975\u00b0 6\t 3.\t Given, sin\u2009\u03b1 + sin\u2009\u03b2 = 2 \t\tA + B = 75\u00b0.\b(1) \t\t \u03b1 = \u03b2 = 90\u00b0. \t\tsec\u2009A = 2 \t\t \u2234 cos2\u03b1 + cos2\u03b2 = cos290\u00b0 + cos290\u00b0 = 0. \t\tsec\u2009A = sec\u200960\u00b0 \t\tA = 60\u00b0. 6\t 4.\t Given, x = a2cos3\u2009\u03b8 and y = b2sin3\u2009\u03b8. \t\tSubstitute the value of A in Eq. (1), \u21d2 x = cos3 \u03b8 and y = sin3 \u03b8 \t\t a2 b2 \t\t60\u00b0 + B = 75\u00b0 y \u21d2 b2 \t\tB = 15\u00b0. \uf8eb x \uf8f62\/3 = cos2 \u03b8; \uf8eb \uf8f62\/3 = sin2 \u03b8 . \uf8ed\uf8ec a2 \uf8f8\uf8f7 \uf8ed\uf8ec \uf8f8\uf8f7 \t\tIn circular measure, \t\tB = 150\u00b0 \u00d7 \u03c0 = \u03c0c . \t\tsin2 \u03b8 + cos2 \u03b8 = \uf8eb x \uf8f62\/3 + \uf8eby \uf8f62\/3 180\u00b0 12 \uf8ed\uf8ec a2 \uf8f8\uf8f7 \uf8ed\uf8ec b2 \uf8f7\uf8f8 6\t 0.\t Given, tan\u2009\u03b8 \u2212 cot\u2009\u03b8 = 7. \t\tWe know that, \t\t\u2234 \uf8ebx \uf8f62\/3 + \uf8eby \uf8f62\/3 = 1. \uf8ec\uf8ed a2 \uf8f8\uf8f7 \uf8ed\uf8ec b2 \uf8f8\uf8f7 \t\ta3 \u2212 b3 = (a \u2212 b)3 + 3ab (a \u2212 b)","16.26 Chapter 16 \t65.\t Given, \t\t \u21d2 sin2\u2009\u03b8 = 1 \t\tcos2\u2009\u03b8 + 2sin2\u2009\u03b8 + 3cos2\u2009\u03b8 + 4sin2\u2009\u03b8 + \u2026 + 200 4 terms = 10025 \t\t \u21d2 sin \u03b8 = 1 ( \u03b8 is acute) \t\t \u21d2 (cos2\u2009\u03b8 + 3cos2\u2009\u03b8 + 5cos2\u2009\u03b8 + \u2026 100 terms) + 2 (sin2\u2009\u03b8 + 2sin2\u2009\u03b8 + \u2026 + 100 terms) = 10025 \t\t \u21d2\u2009\u03b8 = 30\u00b0. \t\t \u21d2 1002cos2\u2009\u03b8 + (1002 + 100) sin2\u2009\u03b8 = 10025 \t\t \u21d2 10000 (cos2\u2009\u03b8 + sin2\u2009\u03b8) + 100sin2\u2009\u03b8 = 10025 \t\t \u2234 sin\u2009\u03b8 \u2212 cos\u2009\u03b8 = sin\u200930\u00b0 \u2212 cos\u200930\u00b0 \t\t \u21d2 100sin2\u2009\u03b8 = 25 1 3 = 1 \u2212 3. \t\t= 2 \u2212 2 2 Hints and Explanation","1172CChhaapptteerr Percentages, PKrionfeimt aatnicds loss, Figure 1.1 Discount and Partnership REmEmBER Before beginning this chapter, you should be able to: \u2022 Understand the concepts of percentage \u2022 Know the terms profit and loss in mathematics \u2022 Understand the concepts of discount and partnership KEY IDEAS After completing this chapter, you should be able to: \u2022 Calculate percentage of absolute values given \u2022 Express percentage as fraction and fraction as percentage and decimal \u2022 Solve numerical problems on percentage \u2022 Make comparison of different percentages in a given problem \u2022 Understand terms, like selling price, cost price, profit and loss \u2022 Know about partnership and its types","17.2 Chapter 17 INTRODUCTION In this chapter, we shall learn the concepts of percentage and their wider applications in day- to-day life situations. In order to solve problems in chapters, like profit and loss, simple interest, compound interest, it is essential to have a thorough understanding of this topic. PERCENTAGE In mathematics, \u2018per cent\u2019 means \u2018for every hundred\u2019. The result of any division in which the divisor is 100, is a percentage. The divisor, that is, 100 is denoted by a special symbol \u2018%\u2019, read as per cent. For example, 10 = 10% 100 25 = 25% 100 x = x% 100 Since any ratio is also a division, each ratio can also be expressed as a percentage. For example, the ratio 1 can be converted into a percentage value: 2 1 = 1\u00d7 50 = 50 = 50 per cent = 50%. 2 2 \u00d7 50 100 Expressing x% as a Fraction Any percentage can be expressed as a decimal fraction by dividing the percentage figure by 100. For example\t\t\t 3=7% 13=070 0.37. =75% 7=5 out of 100 75 = 3 or 0.75. 100 4 Expressing a Fraction a\/b as a Decimal and as a Percentage Any fraction can be expressed as a decimal (i.e., terminating or non-terminating, but recurring), and any decimal fraction can be converted to percentage by multiplying it with 100. 1 = 0.5 = 50% 2 1 = 0.25 = 25% 4 1 = 0.2 = 20% 5 1 = 0.33\u2026 = 33.33\u2026%. 3","Percentages, Profit and Loss, Discount and Partnership 17.3 Problems Based on Basic Concepts Example 17.1 Express 36% as a fraction. Solution 3=6% 1=3060 9 25 \\\\ 36% as a fraction is 9 . 25 Example 17.2 6=4% 1=6040 0.64 Express 64% as a decimal. Solution \\\\ 64% as a decimal is 0.64. Example 17.3 Express 3 as per cent. 20 Solution 3 = \uf8eb 3 \u00d7 100\uf8f6\uf8f7\uf8f8 % = 15% 20 \uf8ed\uf8ec 20 \\\\ 3 as per cent is 15%. 20 Example 17.4 36% of 30 = 36 \u00d7 30 = 10.8 Find 36% of 30. 100 Solution \\\\ 36% of 30 is 10.8. Percentage: A Relative Value When you score 18 marks out of 20 marks in your maths unit test, then it is an absolute value. Let us say that you have scored 90% in the maths unit test; it is understood that you obtained 90 marks out of 100 marks. However, if the maximum marks for the unit test is 50, then the marks you obtained are 90% of 50, or 90 \u00d7 50 = 45. 100","17.4 Chapter 17 Hence, the actual score depends upon the maximum marks of the unit test. It varies with the maximum marks. For example, if the maximum marks are 60, then 90% of 60 = 54. If the maximum marks are 70, then 90% of 70 = 63. As the maximum marks vary, your marks also vary. Hence, percentage is a relative or comparative value. That means, in relation to the total marks, or when compared with the total marks, you score 90% marks. Comparison of Percentages Let us say that in your class 30% of the students are girls, and in Class IX 40% of the students are girls. Can you say that the number of girls in your class is less than the number of girls in Class IX? The answer depends on the total number of students in each class. If there are 50 students in your class, the number of girls in your class = 30 \u00d7 50 = 15 . 100 40 If there are 30 students in Class IX, then the number of girls in Class IX = 100 \u00d7 30 = 12. Although the percentage of girls in your class is less than the percentage of girls in Class IX, the number of girls in your class may be more than that of Class IX. However, you can say that the percentage of girls in your class is more than the percentage of girls in Class IX. But the number of girls in the two classes cannot be compared, if the total number of students in each class is not known. However, when you say that the percentage of girls in your class is less than the percentage of girls in Class IX, you can specify that it is less by 10 percentage points (i.e., 40% - 30% = 10% points). Percentage points is the difference between two percentage values. It is not equal to either percentage increase or percentage decrease. When two absolute values are given, different percentage values can be calculated involving the two values. Let one value be greater than the other. The percentage values involved are: 1.\t One value as a percentage of the other. Example 17.5 x is what per cent of y? Solution Let x = k% of y x = k of y 100 \u21d2 k = x \u00d7 100. y Example 17.6 y y is what percentage of x? x Solution Let y = p% of x \u21d2 p = \u00d7 100.","Percentages, Profit and Loss, Discount and Partnership 17.5 Example 17.7 What percent of 3.6 km is 360 metres? Solution We know that 1 km = 1000 metres. \u21d2 3.6 km = 3.6 \u00d7 1000 = 3600 metres \\\\ The required percentage = \uf8eb 360 \u00d7 100\uf8f6\uf8f7\uf8f8 % = 10% . \uf8ed\uf8ec 3600 Example 17.8 Find the number whose 30% is 36. Solution Let the number be x. Given that 30% of the number is 36. \u21d2 30% of x = 36 \u21d2 30 \u00d7 x = 36 100 \u21d2 x = 36 \u00d7 100 \u21d2 x = 120 30 \\\\ The required number is 120. 2.\t By what per cent is the greater quantity more than the smaller? Percentage more = Greater \u2212 Smaller \u00d7 100% Smaller Example 17.9 By what per cent is the sum of `100 more than the sum of `90? Solution (100 \u2212 90) (100)% = 11 1 % 90 9 That is, the sum of `100 is more than `90 by 11 1 %. 9 Example 17.10 If Anil\u2019s salary is 20% less than Raju\u2019s salary, then by what per cent is Raju\u2019s salary more than that of Anil? Solution Let Raju\u2019s salary be `100. Anil\u2019s salary is 20% less than Raju\u2019s salary.","17.6 Chapter 17 \u21d2 Salary of Anil = 80% of 100 = `80. Raju\u2019s salary is `20 more than that of Anil\u2019s. \u21d2 Now, the required pe=rcentage 82=00 (100)% 25% \\\\ Raju\u2019s salary is 25% more than Anil\u2019s salary. 3.\t By what per cent is the smaller quantity less than the greater? Percentage less = Greater \u2212 smaller \u00d7 100%. greater Example 17.11 Mohit\u2019s weight is 40 kg and Rohan\u2019s weight is 35 kg. By what per cent is Rohan\u2019s weight less than that of Mohit\u2019s? Solution \uf8eb 40 \u2212 35\uf8f6 (100)% = 12.5% \uf8ed\uf8ec 40 \uf8f7\uf8f8 When a quantity changes from time to time, we find percentage change in the quantity. For example, the price of an article is `20 in the year 2005. It became `24 in the year 2006. The percentage in change in the article is 4 \u00d7 100 = 20% increase. 20 Percentage change can be defined as final value \u2212 initial value \u00d7 100. initial value \u2234 Percentage change could be increase or decrease. Example 17.12 In an examination, Mohit secured 60% of the maximum marks which is 45 marks more than the pass marks. If the pass mark is 45%, then find the maximum marks in the examination. Solution Marks secured by Mohit = 60% Pass marks = 45% Difference between the marks obtained and pass marks = (60 - 45)% = 15% Given that Mohit obtained 45 marks more than the pass marks. Let the maximum marks be x. \u21d2 15% of x = 45 \u21d2 x = 45 \u00d7 100 = 300 15 \\\\ The maximum marks in the examination = 300.","Percentages, Profit and Loss, Discount and Partnership 17.7 Example 17.13 The price of an article is decreased by 20%. By what percentage its consumption must be increased so that the expenditure on it increases by 10%? Choose the correct answer from the following options: (a) 10%\u2003\u2003\u2003\u2003(b) 25%\u2003\u2003\u2003\u2003(c) 33 1 % \u2003\u2003\u2003\u2003(d) 37.5% 3 Hints \u2009\u2009\u2009\u2009(i)\t \u0007Let the initial price and initial commodity consumption be `100 and 100 units. \u2009\u2009(ii)\t Let the price of article be `100x. (iii)\tNew price of the article will be 80x. (iv)\tFrom Steps (ii) and (iii), find the required percentage. Example 17.14 In an office, 60% of the employees are female. 30% of the female employees have children and 20% of the male employees have children. What percentage of the employees has children? Choose the correct answer from the following options: (a) 28%\t (b) 26%\t (c) 30%\t (d) 32% Hints \u2009\u2009\u2009\u2009(i)\t Let the total number of employees in the office be 100x. (ii)\tG\u0007 iven, the number of female employees as 60% of 100x. Then, male employees will be 40% of 100x. (iii)\tFind the number of male employees and female employees who have children. (iv)\tRequired percentage = Number of employees who have children \u00d7 100. Total number of employees PROFIT AND LOSS In our everyday life and in the business world, we encounter transactions involving sales and purchases. Every time such a transaction occurs, it may be observed that there is a seller and a buyer involved. The seller sells some things\/goods for a certain amount paid by the buyer. The seller eventually makes some profit or loss in the transaction. This chapter deals with various aspects relating to such transactions of sales and purchases. Cost Price (CP) The price at which an article is purchased is called its cost price. Selling Price (SP) The price at which an article is sold is called its selling price.","17.8 Chapter 17 Profit If the selling price of an article is greater than its cost price, we say that there is profit or gain. Profit = selling price - cost price Percentage of profit is always calculated on the cost price of an article. When SP > CP 1.\t Profit = SP - CP 2.\t SP = CP + Profit 3.\t CP = SP - Profit 4.\t Profit Percentage = Profit (100)% CP 5.\t Profit = Profit Percentage (CP) 6.\t When CP and Profit Percentage are given, SP = (CP ) \uf8eb\uf8ed\uf8ec 100 + Profit Percentage \uf8f6 100 \uf8f8\uf8f7 7.\t When SP and Profit Percentage are given, CP = 100 + 100 (SP) Profit Percentage Loss If the selling price of an article is less than its cost price, we say that there is a loss. Loss = cost price - selling price. Percentage of loss is always calculated on the cost price of the article. When SP < CP: 1.\t Loss = CP - SP 2.\t SP = CP - Loss 3.\t CP = Loss + SP 4.\t Loss Percentage = Loss \u00d7 100% CP 5.\t Loss = Loss Percentage \u00d7 CP 100 Loss Percentage 100 6.\t When CP and Loss Percentage are given, SP = CP \uf8eb \u2212 \uf8f6 \uf8ec\uf8ed \uf8f8\uf8f7 7.\t When SP and Loss Percentage are given, CP = (100 \u2212 SP (100) Loss Percentage) Overheads All the expenditure incurred on transportation, repairs, etc., (if any) are categorized as overheads. These overheads are always included in the CP of the article. \u2002Note\u2002\u2002 When there are two articles having the same cost price and, if one article is sold at a% profit and the other is sold at the same loss per cent, then effectively neither profit nor loss is made. If there are two articles having the same selling price and, one is sold at x% profit and the other is sold at x% loss, effectively, there is always a loss and the loss percentage is \uf8eb x \uf8f62 %. \uf8ec\uf8ed 10\uf8f8\uf8f7","Percentages, Profit and Loss, Discount and Partnership 17.9 Example 17.15 A shopkeeper bought a cycle for `1200 and sold it for `1500. Find his profit or loss percentage. Solution Cost price of the cycle = `1200 Selling price of the cycle = `1500 SP > CP \u21d2 There is a gain. \u21d2 Gain = SP - CP = 1500 - 1200 = `300 \u2234Gain Percentage = Gain (100)% = 300 (100)% = 25% CP 1200 \\\\ The shopkeeper makes a profit of 25%. Example 17.16 Rakesh purchased a TV for `5000. He paid `250 for its transportation. If he sold the TV for `5075, then find his profit or loss percentage. Solution Price at which the TV was bought = `5000 Overheads in the form of transportation = `250 \\\\ The total cost price of the TV = (5000 + 250) = `5250 Selling price of the TV = `5075 SP < CP \u21d2 There is a loss. The amount of loss = CP - SP = 5250 - 5075 = `175. \u2234 Loss percentage = Loss (100)% = 175 (100)% = 10 % = 3.33% . CP 5250 3 \\\\ Rakesh incurred a loss of 3.33%. Example 17.17 By selling 24 pens, Kranthi lost an amount equal to the CP of 3 pens. Find his loss percentage. Solution Let us assume that cost price of each pen is `1. \u21d2 CP of 24 pens = `24 Loss = CP of 3 pens = 3 \u00d7 1 = `3 \u21d2 Loss Percentage = \uf8eb Loss \u00d7 100 \uf8f6 % \uf8ec\uf8ed CP \uf8f8\uf8f7 = 3 \u00d7 100% = 12.5% 24 \\\\ Kranthi\u2019s loss is 12.5%.","17.10 Chapter 17 Example 17.18 Naresh sold two books for `600 each, thereby gaining 20% on one book and losing 20% on the other book. Find his overall loss or gain percent. Solution Selling price of the first book = `600; Profit = 20%. \u21d2 CP = (100 + 100 SP = (100)(600) = `500 Profit Percentage) 100 + 20 The selling price of the second book = `600; Loss = 20% \u21d2 CP = (100 \u2212 100 \u00d7 SP = 100 \u00d7 600 = `750 Loss Percentage) 100 \u2212 20 So, the total cost price of the books = `500 + `750 = `1250. The total selling price of the books = 2 \u00d7 600 = `1200. As the total selling price of the books < the total cost price of the books, there is a loss. Loss = CP - SP = `1250 - `1200 = `50. \u21d2 Loss Percentage = Loss (100)% CP = \uf8eb 50 \uf8f8\uf8f6\uf8f7 100% = 4% \uf8ed\uf8ec 1250 \\\\ Naresh\u2019s loss is 4%. Example 17.19 By selling a ball for `39, a shopkeeper gains 30%. At what price should he sell it to gain 40%? Solution The selling price of the ball = `39; Gain = 30%. \u21d2 CP = \uf8eb 100 + 100 \u00d7 SP \uf8f6 = 100 \u00d7 39 = `30 \uf8ec Gain Percentage \uf8f7 100 + 30 \uf8ed \uf8f8 Now, CP = `30 and gain required = 40%, then \u21d2 SP = CP (100 + Gain Percentage) 100 = ` (30)(140) = `42. 100 \\\\ To gain 40%, the shopkeeper has to sell it for `42. Example 17.20 A merchant marked his product at 50% above the cost price and then allowed 50% discount before selling it. The selling price of the product was `225. What is the profit that he made\/ incurred out of this? Choose the correct answer from the following options: (a) profit of `37.50\t\t (b) profit of `75 (c) loss of `75\t\t\t (d) loss of `37.50","Percentages, Profit and Loss, Discount and Partnership 17.11 Solution Let the cost price of the product be `100x. \\\\ Marked price = `(100x + 50x) = `150x =Discount 15=000 (`150x) `75x Selling price = `75x Given, 75x = 225 x=3 75x < 100x \\\\ A loss was incurred. Loss incurred = `25x = `75. Example 17.21 The cost price and the marked price of a watch are `200 and `300. It was sold at a discount of y%. The profit percentage was 3 y%. Find the value of y from the following options: 2 (a) 16 2 \t (b) 25\t (c) 33 1 \t (d) 20 3 3 Solution Selling price = `300 \uf8eb 1 \u2212 y \uf8f6 = `(300 \u2212 3y) \uf8ec\uf8ed 100 \uf8f7\uf8f8 Selling price = `200 \uf8eb 3 y \uf8f6 \uf8ec\uf8ec1 2 \uf8f7 \uf8ec + \uf8f7 = `(200 + 3y ) 100 \uf8f7 \uf8ed\uf8f8 ( \u2018+\u2019 applies in case of a profit and \u2018-\u2019 applies in case of a loss) 300 - 3y = 200 + 3y 100 = 6y \\\\ y = 16 2 . 3 Partnership The total amount of money required to start a business is called its capital. It is not always possible for a single person to invest huge amount of money. So, two or more persons come together and start business jointly. Such a business is called partnership. The people who jointly runs the business are called partners. The money invested by the partners in the business is called investment.","17.12 Chapter 17 Types of Partnership 1.\t \u0007In general partnership, the period of investment is the same and the partners divide profit or loss in the ratio of their investments. 2.\t I\u0007n compound partnership, the investments and the periods of investment differ. Then their investments reduce to investments per month or year and the profit or loss is divided in the ratio of these converted investments. Example 17.22 Satish and Kranthi started a business with capitals of `12,000 and `18,000, respectively. The business made a profit of `3500. Find the share of Kranthi and Satish in the profit at the end of the year. Solution Investment made by Satish = `12,000 Investment made by Kranthi = `18,000 Ratio of the investments of Satish and Kranthi = 12,000 : 18,000 = 2 : 3. As the period of investment is the same, profit is to be divided in the ratio of their investments. \u21d2 Ratio in which the profit is divided = 2 : 3 Profit = `3500 \\\\ Satish\u2019s share in the profit = 3500 \u00d7 2 = `1400. 5 Kranthi\u2019s share in the profit = 3500 \u00d7 3 = `2100. 5 Example 17.23 Rakesh set up a factory with a capital of `90,000. Ramesh joined him later with an investment of `50,000. The total profit earned at the end of the year was `68,000. Find when Ramesh joined Rakesh as the partner, if Rakesh\u2019s share in the profit is `48,000. Solution Investment of Rakesh = `90,000. Investment period of Rakesh = 12 months. Investment of Ramesh = `50,000. Let investment period of Ramesh be \u2018x\u2019 months. \u21d2 Ratio of their investments = 90,000 \u00d7 12 : 50,000 \u00d7 x = 108 : 5x. Total profit at the end of the year = `68,000. Share of Rakesh in the profit = `48,000. \u21d2 Share of Ramesh in the profit = `(68,000 - 48,000) = `20,000. \u21d2 Ratio of their profits = 48000 : 20000 = 12 : 5 Ratio of investments = Ratio of profits","Percentages, Profit and Loss, Discount and Partnership 17.13 \u21d2 108 : 5x = 12 : 5 \u21d2 108 = 12 5x 5 \u21d2x =9 \u21d2 Investment period of Ramesh = 9 months. \\\\ R\u0007 amesh joined Rakesh as a partner after (12 \u2212 9) months from the commencement of the business, i.e., he joined after 3 months. Example 17.24 Naresh, Gopi and Sarath started a business with initial investments of `10,000, `20,000, and `20,000, respectively. After 6 months, Gopi withdrew an amount of `5000 from his investment. After 3 more months, Sarath brought in `10,000. If at the end of the year, the total amount of profit earned is `36,000, then find the share of each partner. Solution (1) (a)\t Investment of Naresh = `10,000 \t Period of investment = 12 months \t \u21d2 Total investment made by Naresh = `(12 \u00d7 10,000)\b (b)\t Investment of Gopi = `20,000 \t Period of investment = 6 months \t Amount withdrawn = `5000 \t \u21d2 Investment for the remaining 6 months = `(20,000 \u2212 5000) = `15,000 \t \u21d2 Total investment made by Gopi = `(6 \u00d7 20,000 + 6 \u00d7 15,000)\b (2) 3.\t Investment of Sarath = `20,000 \t Period of investment = (6 + 3) = 9 months \t Additional investment = `10,000 \t \u21d2 Investment for the remaining 3 months = `(20,000 + 10,000) = `30,000 \t \u21d2 Total investment made by Sarath = `(9 \u00d7 20,000 + 3 \u00d7 30,000) F\u0007 rom Eqs. (1), (2) and (3), we find the ratio of investments of Naresh, Gopi and Sarath as (12 \u00d7 10,000) : (6 \u00d7 20,000 + 6 \u00d7 15,000) : (9 \u00d7 20,000 + 3 \u00d7 30,000) = 12 : 21 : 27 = 4 : 7 : 9. Total profit at the end of the year = `36,000. Total profit is divided in the ratio of their investments. \\\\ Naresh\u2019s share in the profit = 4 \u00d7 36,000 = `7200 20 Gopi\u2019s share in the profit = 7 \u00d7 36, 000 = `12,600 20 Sarath\u2019s share in the profit = 9 \u00d7 36, 000 = `16,200 20","17.14 Chapter 17 Example 17.25 In a business, P, Q, R and S are four partners. P\u2019s investment is twice R\u2019s investment, Q\u2019s investment is 1 of S\u2019s investment and P and Q invested equally. If the total profit at the end of 4 the year is `13,000, then find the sum of the shares of P and R in the profit. (a) `10,000\t\t (b) `3000\t\t (c) `4000\t\t (d) `5000 Hints \u2009\u2009\u2009\u2009(i)\t Using the given data, find the ratio of the investments of P, Q, R and S. \u2009\u2009(ii)\t Let the investment of A and B be `x each. (iii)\tNow, find the investments of C and D in terms of x. (iv)\tRatio of shares of profits is equal to the ratio of their investments.","Percentages, Profit and Loss, Discount and Partnership 17.15 TEST YOUR CONCEPTS Very Short Answer Type Questions \t1.\t 26% of 640 is ________. 1\t 8.\t If Krishna and Balaram share profits in the ratio 3 : 5 at the end of the year, then the share of \t2.\t If X is 20% more than Y, then what per cent of Y Krishna in the total investment of `16,000 crores is is X? ` _______. \t3.\t Find the value of 99% of 1500 + 45% of 360 + \t19.\t If Nanda sold an article at `40 and earned 100% 55.99% of 3600. profit, then what should be the selling price to earn a profit of 300%? \t4.\t If 1 is 25%, then 9 is _______. 4 16 2\t 0.\t An article is marked up by 100%. If a discount of \t5.\t If 13% of a number is 28, then 26.52% of the same `12 on it is equal to 10%, then the cost price of the number is _______. article is ______. \t6.\t The ratio of incomes of Akshay and Aravind is 2 4 : 3 3 . Income of Aravind is less than that of 2\t 1.\t An increase in the side of a square by 20% results in ______ % increase in its area. Akshay by ________%. 2\t 2.\t When the selling price is `80, there is a loss of 20%. Find the selling price to earn 40% profit. \t7.\t Koutons, an apparel showroom, offers two succes- sive discounts of 50% and 20%. What is the single \t23.\t In a class, 40% of students are girls. Of the total equivalent discount percentage? number of boys, 50% failed in an exam. What per cent of the boys passed in the exam? \t8.\t If the cost price of an article is `64 and its selling price is `80, then profit percentage is ________. \t24.\t Ram and Lakshman started a business by investing `30 lakhs and `48 lakhs, respectively. The ratio in \t9.\t If cost price is `100, marked price is 200% above which they share the profits is _________. the cost price, and discount offered is 50%, then profit per cent is ______. \t25.\t Santan sells a diamond at a loss of 10%. If he had sold it at a profit of 5% he would have earned `37.5 1\t 0.\t If Nityananda scored 25% more than Advaita, then lakhs more. What is the cost price of the diamond? PRACTICE QUESTIONS Advaita scored ______ % less than Nityananda. \t11.\t If 2a = 3b, b = 3 c, and c = 0.8d, then find by what 2\t 6.\t The cost price of a machine is 66 2 % of its selling 4 3 per cent is a less\/more than d. price, then profit per cent is ______. \t12.\t If the cost price of five apples is equal to the selling \t27.\t A person sells 33 1 % of his property at 20% price of 3 apples, then find the profit percentage. 3 1\t 3.\t If the cost price is obtained by multiplying the loss. At what profit per cent should he sell the selling price by 7 , then find the profit percentage. remaining property to earn 20% profit on the 8 whole? 1\t 4.\t This year, the number of children in a colony is 2\t 8.\t If 30% of 40% of x = 60% of 12.5% of 96, then x is ________. three times that of the previous year. What is the percentage increase in the number of children in 2\t 9.\t If two bikes are sold at the same price so that there is a profit of 45% on one bike and a loss of 45% the colony? on the other. The net result of the transaction is _______ (loss\/profit) and it is ______%. 1\t 5.\t A number becomes 63 after it is reduced by 12.5%. The original number is _______. \t16.\t 50% of 50% of 50% of 10% of 560 is ________. 3\t 0.\t Every year there is a 30% hike in Rama\u2019s salary. If his present salary is `2000, then his salary after two 1\t 7.\t When calculated on selling price, profit is found to years will be ` _______. be 25%, find the actual profit percent.","17.16 Chapter 17 Short Answer Type Questions \t31.\t The selling price and the marked price of an arti- question. Find the percentage of marks scored by cle are `132x and `165x, respectively. If the article is marked 65% above the cost price and a discount the students by attempting 120 questions of which of `198 is given, then find the profit on the article. 33 1 % are incorrect. 3 3\t 2.\t The cost of a piece of land increases by 50% every year from 2005 onwards. If the difference in the cost 3\t 8.\t Noel and Mathew save 20% and 30% of their price of the land between the third and the second year is `67,500, then find the cost of the land in 2005. income.\u00a0If their expenditures are equal and Mathew\u2019s income is $5600, then find Noel\u2019s savings (in dollars). \t33.\t In an election, there were only two contestants. 3\t 9.\t In an election, there were only two candidates, A The democrats secured 35% valid votes more than and B. A secured 60% valid votes more than B, and the republicans. If 6% of votes were invalid, then 9% of the total votes were invalid. What percent- what percentage of the total votes polled was in age of the total votes was in favour of A? favour of the democrats? 4\t 0.\t A trader suffered a loss of 15% by selling an article. \t34.\t By selling an article at 1 of its actual selling price, Had he sold it for `100 more, he would have made 4 a profit of 5%. Find the article\u2019s cost price. a trader incurs a loss of 50%. What will be the 4\t 1.\t The price of a commodity is decreased by 25%. By what percentage must its consumption increase so profit per cent if the trader sells the article at its that the expenditure on it remains unchanged? actual selling price? 4\t 2.\t Find the single discount equivalent to successive discounts of 25% and 20%. \t35.\t An electric room heater is sold at $880, after a reduction of 12% in its price. What was the origi- \t43.\t Ajay marked an article at 60% above its cost price. nal price, in dollars, before the reduction? Find the maximum percentage of discount he can offer and still avoid incurring a loss. 3\t 6.\t A dishonest trader declares to sell his goods at cost price, but gives only 960 gms for every 1 kg. Find \t44.\t Find the single discount equivalent to successive the error percentage. discounts of 20% and 10%. PRACTICE QUESTIONS 3\t 7.\t A mock IIT-JEE exam constitutes of 150 questions. 4\t 5.\t Profit percentage is numerically equal to the cost Each correct answer fetches 4 marks. There is price of an article on selling it for `31.25. Find the a penalty of 2 marks for every incorrect answer cost price. and a penalty of 1 mark for every unattempted Essay Type Questions \t46.\t Anthony spends x% of his salary towards expendi- B\u2019s investment is 1 of D\u2019s investment. A and B ture on food, 2x% of the remaining on transport, 3 3x% of the remaining towards various bills, 4x% of the remaining towards loan repayments. If the invested equally. The total profit at the end of the expenditures are denoted as F, T, B and L, respec- tively, if x is 10, then what is the ascending order year is `16,000. Find the sum of the shares of A of these amounts? and C in the profit. 4\t 7.\t Three merchants A, B and C marked three identi- cal articles each at `2000. A sold his article after \t49.\t Amar, Bhuvan and Chetan have some marbles with two successive discounts of 30% each. B sold his them. Bhuvan has 20% more marbles than Amar, article after successive discounts of 40% and 20%. and Chetan has 10% less marbles than Bhuvan. C sold his article after successive discounts of 50% If the total number of marbles with them is 328, and 10%. Find the highest selling price. then find the number of marbles with Bhuvan. \t48.\t In a business, A, B, C and D are the four \t50.\t In a business, Gita and Sita invested in the ratio of partners. A\u2019s investment is thrice C\u2019s investment, 4 : 5. At the end of the year, they earned a profit of `72,000. If Sita\u2019s salary is included, the ratio of their earning is 1 : 2. Find the salary of Sita.","Percentages, Profit and Loss, Discount and Partnership 17.17 CONCEPT APPLICATION Level 1 \t1.\t The population of a city increases by 20% at the \t\t(a) 25%\t\t (b) 20% end of every year. During which of the following years, the population would be doubled? \t\t(c) 33 1 % \t\t (d) 10% 3 \t\t(a) second\t\t (b) third \t8.\t If the cost price of 15 articles is equal to the selling price of 20 articles, find the profit or loss percentage. \t\t(c) fourth\t\t (d) fifth \t2.\t If 20% of a and 40% of b is 230, and 40% of a and \t\t(a) 25% profit\t (b) 20% profit 20% of b is 190, then b is what percentage more or less than a? \t\t(c) 33.33% loss\t (d) 25% loss \t\t(a) 80%\t\t (b) 60% \t9.\t In a test, by scoring 41 2 % of the maximum 3 marks, a student obtains 10 marks more than the \t\t(c) 50%\t\t (d) 40% pass marks. By scoring 30% of the maximum \t3.\t In all the three sections of Woodland High marks, another student scores 4 marks less than the School, there are 50, 70 and 80 students. Those who secured F grade are 10%, 20%, and 30%, pass mark. Find the actual pass percentage. respectively. What percentage of the total students in the school secured F grade? \t\t(a) 11 2 % \t\t (b) 22 1 % 3 6 \t\t(a) 12.5\t\t (b) 15.6 \t\t(c) 33 1 % \t\t (d) 66 2 % 3 3 \t\t(c) 21.5\t\t (d) 23.4 1\t 0.\t The profit made in selling 25 m of a cloth equals \t4.\tIn a test, Arun scored 20% and failed by 10 marks. Bala the selling price of 5 m of that cloth. Find the scored 40% in the same test and obtained 10 marks more than the pass mark. Find the maximum marks. profit percentage. \t\t(a) 25%\t\t (b) 20% \t\t(a) 100\t\t (b) 300 \t\t(c) 33 1 % \t\t (d) 15% PRACTICE QUESTIONS \t\t(c) 400\t\t (d) 200 3 1\t 1.\t Ajay sold two motorbikes for `40,000 each. He \t5.\t On an occasion, 40% of the young men wear grey sold one at 20% profit and the other at 20% loss. hats, 60% of the remaining young men wear black hats. What percentage of the young men wears Find the profit or loss percentage in the whole neither grey hats nor black hats? (No young man wears both grey hat and black hat) transaction. \t\t(a) 2% profit\t (b) 3% loss \t\t(c) 4% loss\t\t (d) No profit, no loss \t\t(a) 12%\t\t (b) 18% 1\t 2.\t A sold an article to B at 30% loss, B sold it to C at \t\t(c) 24% \t\t (d) 25% 20% profit and C sold it to D at 10% profit. If D bought it for `924, then the cost price for A. (in `) \t6.\t If a number x is increased by 20% and then reduced \t\t(a) 1200\t\t (b) 1050 by 20, it results in 160. Instead, if the number x is reduced by 20% and increased by 20, then what \t\t(c) 900\t\t (d) 1000 will be the result? \t13.\t Raja spent 0.5x% of his monthly salary on rent. He \t\t(a) 140\t\t (b) 144 spent x% of the remaining salary on food, 2x% of the remaining salary on transport and 4x% of the \t\t(c) 148\t\t (d) 152 remaining salary on various bills. If these expen- ditures are denoted by R, F, T and S, respectively, \t7.\t The price of an article is increased by 25%. By and if x is 20, then find the ascending order of what percentage must its consumption decrease so these expenditures. that the expenditure on it remains unchanged?","17.18 Chapter 17 \t\t(a) R, S, F, T\t(b) R, F, T, S What will be the profit percent, if a discount of 13% is given? \t\t(c) R, T, F, S\t(d) R, F, S, T 1\t 4.\t In a certain season, the Indian cricket team had a \t\t(a) 12%\t\t (b) 16% 40% success rate in the first 80 matches it played. What is the minimum number of additional \t\t(c) 20%\t\t (d) 24% matches it must play so that it has a 60% success rate for the season? \t20.\t \t\t(a) 30\t\t (b) 40 Year Percentage of the The Population 1995 First Generation of UK (in \t\t(c) 45\t\t (d) 35 2005 Immigrants in UK Millions) \t15.\t If the cost price of 20 articles is equal to the sell- 2% 6x ing price of 15 articles, then find the profit or loss percentage. 2.4% 8x \t\t(a) 20% loss\t\t (b) 25% profit \t\tIf p denotes the percentage increase in the num- (d) 25% loss ber of the first generation immigrants from 1995\u2013 1 2005, and q denotes the percentage increase in the 3 total UK population from 1995\u20132005, find p \u2212 q. \t\t(c) 33 % profit\t \t\t(a) 13 1 %\t\t (b) 26 2 % 3 3 1\t 6.\t Percentage of Population \t\t(c) 33 1 % \t\t (d) 46 2 % First Generation of US 3 3 Immigrants in US Year (in Millions) 2\t 1.\t A shopkeeper marks the price of an article 50% 1990 3% 2000 8k above the cost price and declares a discount of 3.2% 9k 20%. If profit earned is `30, then find the marked price. \t\tIf x denotes the percentage increase in the number \t\t(a) `150\t\t (b) `180 of first generation immigrants from 1990\u20132000, and y denotes the percentage increase in the total \t\t(c) `225\t\t (d) `250 population of US from 1990\u20132000, which of the PRACTICE QUESTIONS following is equal to (x - y)? \t22.\t In a business, P, Q and R are three partners. Thrice P\u2019s investment is equal to twice Q\u2019s investment and \t\t(a) 12.5%\t\t (b) 12.2% R\u2019s investment is equal to twice P\u2019s investment. Q\u2019s period of investment is 4 times P\u2019s period of \t\t(c) 9.6%\t\t (d) 7.5% 3 investment and is twice R\u2019s period of investment. 1\t 7.\t Trader A gives a single discount of 30% and trader If the total profit at the end of the year is `52,000, B gives two successive discounts of 20% and 10% find the sum of the shares of P and Q in the profit. on an identical article. If the discount given by A is (in `) `600 more than the discount given by B, find the marked price of the article. \t\t(a) 32,000\t\t (b) 36,000 \t\t(a) `1500\t\t (b) `3000 \t\t(c) 40,000\t\t (d) 28,000 \t\t(c) `30,000\t\t (d) `600 \t23.\t Ratan spends 70% of his income. His income increases by 25%, and his expenditure also increased \t18.\t X sells an article to Y at 15% profit. Y sells it to Z by 25%. Find the percentage increase in his savings. at 10% profit. What is X\u2019s cost price, if Y makes a profit of `23? \t\t(a) 25\t\t (b) 30 \t\t(a) `230\t\t (b) `200 \t\t(c) 10\t\t (d) No change \t\t(c) `150\t\t (d) `180 \t24.\t Mahesh sold an article for `39 and obtained profit percentage which is numerically equal to its cost 1\t 9.\t When a discount of 10% is given on the marked price (in rupees). Find the cost price of the article. price of an article, the gain of the trader is 20%.","Percentages, Profit and Loss, Discount and Partnership 17.19 \t\t(a) `28\t\t (b) `32 2\t 6.\t A trader marks his product 30% above his cost price, and then offers a 30% discount. Find his cost \t\t(c) `30\t\t (d) `35 price if he incurs a loss of `900. (in `) \t25.\t The selling price of an article after giving three \t\t(a) 12,000\t\t (b) 10,000 successive discounts is `7560. If the marked price is `15,000, then which of the following can be the \t\t(c) 9000\t\t (d) 8000 successive discounts? \t27.\t The loss made in selling 20 m of a cloth equals \t\t(a) 8, 16, 24 the cost price of 4 m of that cloth. Find the loss percentage. \t\t(b) 5, 10, 15 \t\t(a) 20%\t\t (b) 25% \t\t(c) 10, 20, 30 (d) 40% \t\t(c) 33 1 % \t\t \t\t(d) 15, 30, 45 3 Level 2 \t28.\t Three merchants, P, Q and R marked three iden- 3\t 2.\t A B tical articles each at `4000, respectively. P sold 24 36 his article after two successive discounts of 40% Name of the class 60 80 each. Q sold it after successive discounts of 50% and 30%. R sold it after successive discounts Number of girls of 60% and 20%. Find the least selling price. (in `) Number of girls as a percentage of total number of students \t\t(a) 1320\t\t (b) 1280 \t\tAs per the information given in the above table, approximately by what percentage is the total \t\t(c) 1440\t\t (d) 1200 number of students in class A is less than those in class B? \t29.\t A shopkeeper marks the cost of two identical arti- \t\t(a) 9%\t\t (b) 10% PRACTICE QUESTIONS cles, one 100% above the cost price and the other 50% above the cost price. If a discount of 20% is \t\t(c) 11%\t\t (d) 13% allowed on each of them, then find the overall profit percentage. \t33.\t A person bought two articles for `1800. He sold the first article at a profit of 25% and the second at \t\t(a) 10%\t\t (b) 20% a loss of 20%. On the whole there is neither loss nor gain. Find the cost price of the second article. \t\t(c) 30%\t\t (d) 40% \t\t(a) `800\t\t (b) `1000 3\t 0.\t The profit made in selling 5 m of a cloth equals \t\t(c) `900\t\t (d) `1200 the cost price of 2 m of that cloth. Find the profit percentage. 3\t 4.\t The ratio of the marked price and the cost price of an article is 5 : 3. If a loss of 2a% is obtained after \t\t(a) 30%\t\t (b) 40% giving a discount of 4a%, then find a. \t\t(c) 33 1 % \t\t (d) 45% \t\t(a) 14 6 \t\t (b) 12 3 3 7 7 \t31.\t The price of an article is increased by 20%. By \t\t(c) 13 2 \t\t (d) 14 2 what percentage must its consumption be reduced 7 7 so that the expenditure on it reduces by 10%? \t35.\t Three persons X, Y and Z started a business with \t\t(a) 20%\t\t (b) 30% investments in the ratio of 3 : 2 : 4. The ratio of their periods of investments is 5 : 6 : 7. The dif- \t\t(c) 25%\t\t (d) 15% ference in the shares of profits of X and Z is what","17.20 Chapter 17 percentage of the share of profit of Y at the end of \t\t(a) `22,000\t\t (b) `11,000 the year? (Approximately) \t\t(c) `16,500\t\t (d) `33,000 \t\t(a) 120%\t\t (b) 108.33% 4\t 2.\t Ramapada has just enough money to purchase either 30 pens or 50 pencils. He decides to spend \t\t(c) 115.25%\t\t (d) 125.66% only 80% of his money and buys 10 pens. At the maximum, how many pencils can he buy with the \t36.\t Ajay invested `m for 7 months and `n for the remaining money that he has? remaining period. Sohail invested `n for the first 9 months and `m for the remaining period. If at \t\t(a) 23\t\t (b) 24 the end of the year, they share profits equally, then what is the relation between m and n? \t\t(c) 25\t\t (d) 26 \t\t(a) m = n + 1\t (b) m - n = 2 \t43.\t A trader claims to sell his goods at cost price. But, he gives only 900 g for every kg. Find his profit \t\t(c) m = n\t\t (d) m + n = 2 percentage. 3\t 7.\t Ramesh spends 60% of his income. His income \t\t(a) 11 1 % \t\t (b) 9 1 % increases by 40%, and also his expenditure by 40%. 9 11 The percentage of increase in his savings is ______. \t\t(a) 20%\t\t (b) 30% \t\t(c) 10%\t\t (d) 12 2 % 3 \t\t(c) 40%\t\t (d) 50% 4\t 4.\t Amish sold an article at two-thirds of the marked 3\t 8.\t A dishonest shopkeeper sells his items at cost price. 2 But, for every kg he gives 200 gm less. His profit price and suffered a loss of 16 3 %. Find the percentage is ______. percentage of profit, if he sold the article at the \t\t(a) 20%\t\t (b) 25% marked price. \t\t(c) 30%\t\t (d) 15% \t\t(a) 20%\t\t (b) 25% 3\t 9.\t Preetam bought two mobile phones for `4800. He \t\t(c) 16 2 % \t\t (d) 33 1 % sold the first mobile phone at a loss of 15%, and 3 3 the second at a profit of 25%. On the whole, there PRACTICE QUESTIONS was neither loss nor gain. The cost price of the 4\t 5.\t Raman suffered a loss of 10% by selling an article. second mobile phone is ______. Had he sold it by `180 more, he would have made a profit of 2%. Find his cost price (in `). \t\t(a) `1800\t\t (b) `3000 \t\t(a) 1350\t\t (b) 1800 \t\t(c) `1200\t\t (d) `2400 \t\t(c) 1650\t\t (d) 1500 \t40.\t The selling price of a TV, after giving two successive \t46.\t Anil bought certain number of books at the rate of discounts, is `15,840. If the marked price is `20,000, then which of the following could be the successive 12 books for `18 and sold them at the rate of 18 discounts given on the marked price of the TV? books for `30. Find his profit\/loss percentage. \t\t(a) 10, 15\t\t (b) 12, 15 \t\t(a) 9 1 % \t\t (b) 10% 11 \t\t(c) 10, 12\t\t (d) 15, 18 \t\t(c) 11 1 % \t\t (d) 12 1 % 9 2 4\t 1.\t In a business, A, B and C are three partners. Twice \t47.\t In an election, there were only two contestants P A\u2019s investment is equal to C\u2019s investment. Also, B\u2019s 1 and Q. 14% of the total votes polled were invalid. investment is equal to 2 of A\u2019s investment. A\u2019s The number of valid votes secured by P was 15% period of investment is equal to 4 times C\u2019s period more than that secured by Q. What percentage of of investment, and A and B invested for the same the total votes was cast in favour of Q? period. If the total profit at the end of the year is \t\t(a) 48%\t\t (b) 37.5% `44,000, then find the sum of the shares of A and \t\t(c) 40%\t\t (d) 31.5% B in the profit.","Percentages, Profit and Loss, Discount and Partnership 17.21 Level 3 \t48.\t Bindu goes to a shop to buy a gift costing `1500. What percentage of the married employees are On her request, the shopkeeper allows two post-graduates? successive discounts of x% and y%. (x < y). Bindu buys the gift for `1188 including sales tax of 10%. \t\t(a) 36%\t\t (b) 32% Which of the following could be the discount rates offered by the shopkeeper? \t\t(c) 30%\t\t (d) 27% \t54.\t Amar, Bhavan and Chetan divide a certain amount \t\t(a) 15%, 20%\t (b) 20%, 25% among themselves. The average of the amounts \t\t(c) 20%, 30%\t (d) 10%, 20% with them is `1180. Amar\u2019s share is 33 1 % more 3 4\t 9.\t In the year 2001, the population in a village is x. 2 Every year, the population increases by 10%. In than that of Bhavan\u2019s and 16 3 % less than that of which year, for the first time, will the population of the village be at least 50% more than that of year Chetan\u2019s. Find Amar\u2019s share. (in `) 2001? \t\t(a) 1050\t\t (b) 1200 \t\t(a) 2005\t\t (b) 2006 \t\t(c) 1350\t\t (d) 1500 \t\t(c) 2004\t\t (d) 2007 5\t 5.\t In a certain season, the Indian cricket team had won 30% of the first 60 matches it had played. 5\t 0.\t In a family, a person saves 30% of his income. If his Find the minimum possible number of additional salary is increased by 20% and savings are decreased matches it should play to achieve a success rate of by 20%, then find the percentage increase in the 44% in that season. expenditure. \t\t(a) 20\t\t (b) 15 1 1 \t\t(a) 34 4 % \t\t (b) 37 7 % \t\t(c) 25\t\t (d) 30 \t\t(c) 41 1 % \t\t (d) 43 1 % 5\t 6.\t Mohan and Sohan started a business. Mohan was 7 3 a sleeping partner in the business. Sohan, being the working partner, took a certain monthly salary. 5\t 1.\t A sold an article to B at 10% profit. B sold it to C At the end of the first year, the total amount of PRACTICE QUESTIONS at 20% profit. Find the price at which A bought profit was `3,00,000. The ratio of Mohan\u2019s and the article, if B\u2019s profit is `44. (in `) Sohan\u2019s shares was 9 : 11. If Sohan\u2019s annual salary was excluded, the ratio of their shares become 9 : \t\t(a) 150\t\t (b) 200 7. Find the monthly salary of Sohan. (in `) \t\t(c) 250\t\t (d) 100 \t52.\t A person spends 25% of his salary on house rent, \t\t(a) 5400\t\t (b) 5000 20% of the remaining salary on clothes, 16 2 % of \t\t(c) 7500\t\t (d) 7800 3 the remaining on petrol and 30% of the remaining 5\t 7.\t X and Y are two natural numbers. The sum of thrice of X and twice of Y is 230. If 3X increases on food. If after incurring the above expenditure by 40% and 2Y increases by 30%, then their sum will increase by 84. If X decreases by 40% and Y his savings are `147, then find his salary. decreases by 30%, then their sum will be ______. \t\t(a) `480\t\t (b) `300 \t\t(c) `350\t\t (d) `420 \t\t(a) 58\t\t (b) 66 5\t 3.\t In an office, 30% of the employees are unmar- \t\t(c) 52\t\t (d) 46 ried; 20% of these employees are post-graduates. The number of married employees in the office 5\t 8.\t Giri sold two books. The selling price of a book who are post-graduates is 312 times that of the equals the cost price of the second book. He sold unmarried employees who are post-graduates. the first book at 10% profit and the second book at 10% loss. Find the overall profit\/loss percentage.","17.22 Chapter 17 \t\t(a) 5 % profit\t\t (b) 5 % loss \t60.\t In a class, 45% of the students drink pulpy 21 21 orange and 90% of the remaining students drink Maaza. No student drinks both Maaza and \t\t(c) 10 % profit\t\t (d) 10 % loss pulpy orange. Find the percentage of students 21 21 in the class who drink neither Maaza nor pulpy \t59.\t P sold an article at 20% profit to Q. Q sold it at orange. 10% profit to R. The profit made by Q was `24 \t\t(a) 4.5% less than the profit made by P. Find the cost price \t\t(b) 6.5% of the article for P. (in `) \t\t(c) 7.5% \t\t(a) 250\t\t (b) 300 \t\t(d) 5.5% \t\t(c) 360\t\t (d) 200 PRACTICE QUESTIONS","Percentages, Profit and Loss, Discount and Partnership 17.23 TEST YOUR CONCEPTS Very Short Answer Type Questions \t1.\t 166.4 \t16.\t 7 \t2.\t 120% 1\t 7.\t 33 1 % 3 \t3.\t 3662.64 \t18.\t `6000 crores \t4.\t 56.25% \t19.\t `80 \t5.\t 57.12 \t20.\t `60 \t6.\t 8.33% \t21.\t 44% \t7.\t 60% \t22.\t `140 \t8.\t 25% \t23.\t 30% \t9.\t 50% 2\t 4.\t 5 : 8 \t10.\t 20% 2\t 5.\t 250 lakhs 1\t 1.\t 10% less 2\t 6.\t 50% 2 1\t 2.\t 66 3 % 2\t 7.\t x = 40% 13.\t 14 2 % 2\t 8.\t 60 7 2\t 9.\t loss, 20.25% 1\t 4.\t 200% \t30.\t `3380 1\t 5.\t 72 Short Answer Type Questions 3\t 9.\t 56 \t31.\t 192 4\t 0.\t 500 3\t 2.\t `60,000 \t33.\t 54 4\t 1.\t 33 1 % \t34.\t 100% 3 3\t 5.\t 1000 ANSWER KEYS \t36.\t 4% 4\t 2.\t 40% 3\t 7.\t 35% 3\t 8.\t $980 4\t 3.\t 37.5% \t44.\t 28% 4\t 5.\t 25% Essay Type Questions 4\t 9.\t 120 5\t 0.\t `18,000 \t46.\t F, T, L, B 4\t 7.\t 980 4\t 8.\t 4000","17.24 Chapter 17 CONCEPT APPLICATION Level 1 \t1.\u2002(c)\t 2.\u2002 (a)\t 3.\u2002 (c) \t 4.\u2002 (a)\t 5.\u2002 (c)\t 6.\u2002 (a)\t 7.\u2002 (b)\t 8.\u2002 (d)\t 9.\u2002 (c) \t 10.\u2002 (a) \t11.\u2002 (c)\t 12.\u2002 (d)\t 13.\u2002 (b) \t 14.\u2002 (b)\t 15.\u2002 (c)\t 16.\u2002 (d)\t 17.\u2002 (c)\t 18.\u2002 (b)\t 19.\u2002 (b)\t 20.\u2002 (b) \t21.\u2002(c)\t 22.\u2002 (b)\t 23.\u2002 (a)\t 24.\u2002 (c)\t 25.\u2002 (c)\t 26.\u2002 (b)\t 27.\u2002 (a) Level 2 30.\u2002 (b)\t 31.\u2002 (c)\t 32.\u2002 (c)\t 33.\u2002 (b)\t 34.\u2002 (d)\t 35.\u2002 (b)\t 36.\u2002 (c)\t 37.\u2002 (c) 40.\u2002 (c)\t 41.\u2002 (b)\t 42.\u2002 (a)\t 43.\u2002 (a)\t 44.\u2002 (b)\t 45.\u2002 (d)\t 46.\u2002 (c) \t 47.\u2002 (c) \t28.\u2002 (b)\t 29.\u2002 (d)\t \t38.\u2002 (b)\t 39.\u2002 (a)\t Level 3 50.\u2002 (b)\t 51.\u2002 (b)\t 52.\u2002 (d)\t 53.\u2002 (c)\t 54.\u2002 (b)\t 55.\u2002 (b)\t 56.\u2002 (b)\t 57.\u2002 (a) 60.\u2002 (d) \t48.\u2002 (d) \t 49.\u2002 (b)\t \t58.\u2002 (d) \t 59.\u2002 (b)\t ANSWER KEYS","Percentages, Profit and Loss, Discount and Partnership 17.25 CONCEPT APPLICATION Level 1 P \uf8eb\uf8ed\uf8ec1 + r \uf8f6\uf8f7\uf8f8 n 100 \t1.\t Use the formula, A= . \t\t(ii)\tIn the given conditions, trader suffer loss. \t2.\t 20% a + 40% b = 230. \t\t(iii)\tLoss percentage = (Profit % or loss %)2 100 \t\t40% a + 20% b = 190. Find a and b. \t12.\t (i)\tLet CP of A be `100. \t3.\t Number of students who obtained grade F \u00d7 100. \t\t(ii)\tLet CP for A be `x. The total number of students \t\t(iii)\tx \uf8ed\uf8ec\uf8eb 17000\uf8f7\uf8f6\uf8f8 \uf8ec\uf8ed\uf8eb 110200\uf8f7\uf8f6\uf8f8 \uf8eb\uf8ec\uf8ed 110100\uf8f6\uf8f7\uf8f8 = 924. \t4.\t Difference in the percentages = Difference in the 1\t 3.\t (i)\tLet Raja\u2019s monthly salary be `100. marks. \t5.\t (i)\tLet the total number of young men be 100. \t\t(ii)\tLet the salary of Raja be `100x. \t\t(ii)\tLet the number of young men who attend the \t\t(iii)\tR = 10% of `100x = `10x. party be 100x. \t\t(iv)\tSimilarly, find F, T and S, and then compare. \t\t(iii)\tFind number of young men who wear grey 1\t 4.\t (i)\tFind the number of matches won out of 80 hats, and also find that of who wear black hats. matches. Minimum number of additional matches is equal to the number of matches to be won. \t6.\t Find x from the first statement. \t7.\t Let the initial price be `100 and initial consump- \t\t(ii)\tFirst, find the number of matches won out of tion be 100 units. 80 matches played. \t8.\t (i)\tFind SP and CP of 20 articles by taking CP of \t\t \tThat is, 40 \u00d7 80 = 32. Hints and Explanation 1 article = `x. 100 \t\t(ii)\tAs the CP of 15 articles is equal to the SP of 20 \t\t(iii)\tTo get minimum number of matches to be articles, trader suffers loss. played, it has to win all the additional matches. \t\t(iii)\tLet C\u2009=\u200915 and S\u2009=\u200920. Loss % = \uf8eb S \u2212C \uf8f6 \u00d7 100. \t\t(iv)\tLet the required number of matches = x. \uf8ec\uf8ed S \uf8f7\uf8f8 \t\t \t\u21d2 (32 + x) \u00d7 100 = 60. (8 + x) \t9.\t Let m be the maximum marks and p be the pass marks. \t15.\t (i)\tFind SP and CP of 15 articles by taking CP of one article as `x. 41 2 m 3 \u00d7 30\u00d7 m \t\t(ii)\tAs the CP of 20 articles is equal to SP of 15 100 articles, trader earns profit. \t\t(ii)\tGiven, 100 = p + 10 and = p \u2212 4. \t\tFrom the above equations, we obtain the values of \t\t(iii)\tLet C = 20, and S = 15. m and p. \t\t \tProfit% \uf8eb S \u2212C \uf8f6 100. = \uf8ed\uf8ec S \uf8f7\uf8f8 \u00d7 1\t 0.\t (i)\tLet SP of 1 m of cloth be `x. \t\t(ii)\tLet SP of 25 m of a cloth be `25x. 1\t 6.\t (i)\tFind x and y using the given information. \t\t \t\\\\ Profit = `5x. \t\t(ii)\tFirst, find population of the first generation immigrants in 1990 and 2000, i.e., 3% of 8k \t\t(iii)\tNow find the CP, and then the profit %. and 3.2% of 9k. \t11.\t (i)\tWhenever SP is same and % of loss = % of \t\t(iii)\tThen find percentage increase (x). profit = x%, there is always loss, and loss% = x2 . \t\t(iv)\ty = 1k (100), and then find (x \u2212 y). 100 8k","17.26 Chapter 17 \t17.\t (i)\tLet MP of A be `100, then find the difference \t22.\t (i)\tFind the ratio of investments and the ratio of in the discount given by A and B. time periods. \t\t(ii)\tLet the MP be `x. \t\t(ii)\tLet P\u2019s investment be `x. \t\t(iii)\tSuccessive discounts 20% and 10% is equiva- \t\t(iii)\tNow, find investments of Q and R in terms of lent to a single discount of 28%. x with the given data. \t\t(iv)\tNow, 30% of x \u2212 28% of x = `600. \t\t(iv)\tLet the time period of investment of R be y months. 1\t 8.\t (i)\tLet CP of x be `100, then find SP of x. \t\t(v)\tNow, find time periods of investment of P \t\t(ii)\tLet CP for X be `100x. and Q. \t\t(iii)\tFind CP and SP for Y. Then find profit earned \t\t(vi)\tRatio of shares of profits is equal to the ratio by Y (in x) and compare it with `23. of product of investments and investment periods. \t\t(iv)\tCP of Y = SP of X. 2\t 6.\t (i)\tLet CP of the product be `100, then find MP \t19.\t Assume the cost price be `100. and SP. \t\tm \uf8eb 90 \uf8f6 = 120. \t\t(ii)\tLet the CP be `100x. \uf8ed\uf8ec 100 \uf8f8\uf8f7 \t\t(iii)\tMP = 130x and SP = 70% of 130x. \t20.\t (i)\tFind p and q using the given information. \t\t(iv)\tCP - SP = 900, find x. \t\t(ii)\tFirst, find the population of the first genera- tion immigrants in 1995 and 2005, i.e., 2% of 2\t 7.\t (i)\tLet CP of 1 m cloth be `x, then the amount of 6x and 2.4% of 8x. loss and SP. \t\t(iii)\tThen find percentage increase (q). \t\t(ii)\tLet the CP of 20 m of a cloth be `20x. Hints and Explanation \t\t(iv)\tP = 2x (100), and then find (p \u2212 q). \t\t(iii)\tSo, loss = `4x. 6x \t\t(iv)\tNow, find loss percentage. \t21.\t Assume the cost price be `100, then marked price is `150. Level 2 \t28.\t (i)\tFind the discounts given by P, Q and R. \t31.\t (i)\tLet the initial price and initial consumption be `100 and 100 units, respectively. \t\t(ii)\tFind the SP for P, Q and R by using the following formulae. \t\t(ii)\t(Consumption) (Price of an article) = Total expenditure. (100 \u2212 d ) SP = 100 MP (OR) \t\t(iii)\tLet consumption be 100 articles and rate be \t = `100. \t\t SP (100 \u2212 d1 ) (100 \u2212 d2 ) 100 100 MP \t\t(iv)\tGiven, rate = `80 and total expenditure = `9000. Find the consumption by using the \t\t(iii)\tCompare the SP\u2019s. formula which is mentioned in (i). 2\t 9.\t Marked price of the first article = `200. \t\t(v)\tFind the percentage decrease in the \t\tMarked price of the second article = `150. consumption. 3\t 0.\t (i)\tLet CP of 1 m cloth be `x. \t\t(ii)\tLet the CP of 5 m of a cloth be `5x. \t32.\t (i)\tFind the total number of students in class A \t\t(iii)\tSo, profit = `2x. and class B. \t\t(iv)\tNow, find the profit percentage. \t\t(ii)\tTotal number of students in class A = \uf8eb 24 \uf8f6 \u00d7 100. \uf8ed\uf8ec 60 \uf8f8\uf8f7","Percentages, Profit and Loss, Discount and Partnership 17.27 \t\t(iii)\tSimilarly, find the total number of students in \t45.\t Let his cost price be `100x. class B. \t\tActual SP = 90% of (100x) \t\t(iv)\tFind the difference between the total number \t\tConsidered SP = 102% of (100x) of students in both the sections, and then find percentage difference with respect to the total \t\t102% of (100x) = 90% of (100x) + 180 number of students in class B. \t\t12% of (100x) = 180 \t41.\t Ratio of profits = (Ratio of investments) \u00d7 (Ratio \t\t\u2234100x = 180 (100) = 1500 of time periods) 12 4\t 2.\t Assume that Ramapada have `150, then find the \u2234Cost price = `1500. CP of pen and pencil. \t46.\t While calculating the profit\/loss percentage, 4\t 3.\t Let the cost price be `1000x\/kg. we must consider equal number of books being \t\tThe selling price of 900 g = The cost price of bought and sold. 1000\u00a0g. \t\tThe cost price of each bo=ok `=1182 ` 3 . 2 \t\t \\\\ The selling price of 900 g = `1000x. \t\tThe selling price of each bo=ok `=1380 ` 5 . \t\tThe cost price of 900 g 900 (`1000x) `900x 3 = 1000 = 3 5 \t\tProfit in selling 900 g = `100x. \t\tAs 2 < 3 , a profit is made. \t=\tProfit % 19=0000xx (100%) 11 1 %. 5 \u2212 3 9 3 2 Profit % = \u00d7 (100%) 4\t 4.\t Let the marked price of the article be `100x. \t\t 3 2 x 2 200 \t\t \\\\ Selling price = 3 \u00d7 ( `100x ) = ` 3 x \b(1) 1 \t\tLet the cost price be `100y. = 6 \u00d7 (100%) = 11 1 %. Hints and Explanation 3 9 16 2 3 `1060y 2 Loss = \u00d7 ( `100y ) = 100 4\t 7.\t Let the total number of votes casted be 100x. \u21d2 Selling price = `100y \u2212 `1060y \t\tThe number of inv=alid votes 11=040 (100x) 14x. \t\t = `500y \b(2) \t\tThe number of valid votes = 100x - 14x = 86x. 6 \t\tLet the number of votes secured by Q be q. \t\t5060y 2=030x (from Eqs. (1) and (2))y 4 x \t\tNumber of votes secured by P = q. 5 \uf8ec\uf8ed\uf8eb1 + 15 \uf8f6 23 q 23 q q 86x \uf8eb 4x \uf8f6 100 \uf8f7\uf8f8 = 20 \u21d2 20 + = \uf8ed\uf8ec 5 \uf8f7\uf8f8 \t\t\u2234 Cost price = 100 = `80x 43 20 \t\tIf he sold the article at marked price. \t\t q = 86x \u21d2 q = 40x \t\t \\\\ Profit percentage = 100x \u2212 80x \u00d7 (100%) = 25%. \t\t \\\\ The required=percentage 1=4000xx (100%) 40%. 80x Level 3 \t49.\t Let the population of the village in the year 2001 \t\t(ii)\tLet CP for A be `100x. be 100 and proceed. \t\t(iii)\tFind CP and SP for B, and then find profit 5\t 0.\t Assume the income of the person to be `100 and earned by B (in x) and compare it with `44. proceed. \t\t(iv)\tCP of B = SP of A. \t51.\t (i)\tLet CP of A be `100.","17.28 Chapter 17 \t52.\t Assume that the salary of the person to be `100 18 + y \u00d7 (100)% = 44% and follow the data given in the problem. 60 + y 5\t 3.\t Let the total number of employees be 100x. 1800 + 100y = 2640 + 44y 30 The number of unmarried employees = 100 (100x ) 56y = 840 = 30x. \t\t y = 15 \t\tThe number of unmarried post-graduates 5\t 6.\t Let Mohan\u2019s and Sohan\u2019s shares be `9x and `11x, = 1=2000 (30x) 6x. post-graduates respectively. \t\tThe number of married \t\t9x + 11x = 300000 = \uf8eb 3 1\uf8f6 (6x ) = 21x. \t\tx = 15000 \uf8ec\uf8ed 2\uf8f7\uf8f8 \t\tSohan\u2019s share excluding his annual salary = 7x. \t\tThe number of married employees = 100x - 30x \t\t \\\\ Sohan\u2019s Annual salary = 11x - 7x = 4x = 70x. = `60,000. \t\tThe required p=ercentage 72=01xx (100)% 30%. \t\tSohan\u2019s monthly=salary `=6102000 `5000. \t54.\t Let the amounts with Amar, Bhavan and Chetan \t57.\t 3X + 2Y = 230\b (1) be `a, `b and `c, respectively. \t\tIf 3X increases by 40% and 2X increases by 30%, a +b+ c 3 = 1180 total increase = 40 (3X ) + 30 (2Y ) 100 100 a + b + c = 3540 40 30 \uf8eb 33 1 \uf8f6 \uf8eb 16 2 \uf8f6 \u2234 100 (3X ) + 100 (2Y ) = 84 \uf8ec\uf8ec1 3 \uf8f7 \uf8ec\uf8ec1 3 \uf8f7 Hints and Explanation a = b \uf8ec + \uf8f7 = c \uf8ec \u2212 \uf8f7 \t\t 1.2X + 0.6Y = 84 100 \uf8f7 100 \uf8f7 \t\tDividing both sides by 0.6, 2X + Y = 140 \uf8ed \uf8f8\uf8ed \uf8f8 a = 4 b = 5 c \t\t \\\\ Y = 140 - 2X\b(2) 3 6 \t\t \\\\ 2Y = 280 - 4X 3 6 b = 4 a and c = 5 a \t\t(1) \u21d2 2Y = 230 - 3X a b c 59 a \t\t \\\\ 280 - 4X = 230 - 3X 20 + + = \t\t50 = X 59 a = 3540 (given) \t\t(2) \u21d2 Y = 40 20 \t\tThe required sum = X \uf8eb\uf8ec\uf8ed1 \u2212 40 \uf8f6 + Y \uf8eb\uf8ed\uf8ec1 \u2212 30 \uf8f6 a = (50)(0.6) + (40) 100 \uf8f8\uf8f7 100 \uf8f7\uf8f8 20 = 60 \t\t a = 1200. \t\t(0.7) = 58. \t55.\t Let the number of matches played be 60 + x. This 5\t 8.\t Let the cost price of the first book be `100x. is minimum when x is minimum. \t\tThe profit m=ade on it 11=000 (`100x) `10x \t\tIts selling price = `110x \t\tAs the target was achieved for the minimum value of x, all the x matches must have been won. \t\tLet the minimum (x) = y. \t\tThe cost price of the second book = `110x \t\t \\\\\u2009The total number of matches won \t\tThe loss suf=fered on it 11=000 (`111x) `11x \t\tIts selling price = `99x = 30 (60) + y = 18 + y 100","Percentages, Profit and Loss, Discount and Partnership 17.29 \t\tTotal cost price = `210x \t60.\t Let the strength of the class be 100x. \t\tTotal selling price = `209x \t\tThe number of students who drink pulpy orange \t\tAs 210x > 209x, on overall loss is made. =\t\t 1=4050 (100x) 45x. \t\tOverall loss = `x \t\tThe number of students who drink Maaza \t\t \\\\ Overall loss percentage = x \u00d7 (100)% = 1201 % . 90 (100x 45x ) 210x 100 = \u2212 \t59.\t Let the cost price for P be `100x. \t=\tP\u2019s profit 12=000 (`100x) `20x \t\t= 9 (55x ) = 49.5x \t\tThe selling price for P = `120x 10 \t\tNo student drinks both Maaza and pulpy orange. \t\tThe cost price for Q = The selling price for P = \t\tThe number of students of the class who drink `120x neither Maaza nor pulpy orange \t\t=Q\u2019s profit 11=000 (`120x) `12x \t\t= 100x - 94.5x = 5.5x \t\tGiven, 12x = 20x - 24 \t\tThe required=percentage 15=0.50xx (100)% 5.5%. \t\t\u21d2 3 = x \u21d2 100x = 300. Hints and Explanation","1182CChhaapptteerr CSKaoinlsetesmoTfaatlixicvsainngd Index REmEmBER Before beginning this chapter, you should be able to: \u2022 Understand the term \u2018tax\u2019 and its importance \u2022 Know development and welfare activities done by the government \u2022 Explain the phrase \u201bcost of living\u2019 KEY IDEAS After completing this chapter, you should be able to: \u2022 Understand the term \u2018sales tax\u2019 and its functions \u2022 Know what is value-added tax (VAT) \u2022 Work on cost of living index \u2022 Solve word problems based on tax Figure 1.1","18.2 Chapter 18 INTRODUCTION The government provides primary health care, free education, maintenance of infrastructural facilities, like roads and bridges. For all these activities, the government needs huge funds. To meet the expenditure incurred on these developmental and welfare activities, the government levies or imposes various taxes, like central excise, sales tax, octroi and income tax. In this chapter, we will deal with sales tax and the cost of living indexes. Sales Tax Sales tax is levied at a specified rate on the net selling price of a commodity. It varies from commodity to commodity, and also from state to state. The selling price is the marked price when discount offered is zero. In case a discount is allowed on a commodity, the net selling price would be the marked price minus discount. The traders or business organizations, which collect sales tax, submit monthly sales tax returns to the sales tax office, under whose jurisdiction their business operations are carried out. Sales tax has been replaced by value-added tax in many states. Value-Added Tax (VAT) VAT is a multi-point levy on the goods in a supply chain, with the facility to set-off input tax, that is, only the value addition in the hands of the entities is subject to tax. For an instance, a dealer purchases goods worth `75 from another dealer, and a tax of `3 at 4% is charged on the bill. He sells the goods for `100, on which he charges tax of `4 at 4%. Since the tax levied on `75, i.e., `3 is already paid, a tax of `4 - `3 = `1 has to be paid by the buyer in the second transaction. In the second transaction, the tax is levied on the value addition, i.e., `100 - `75 = `25. Here, 4% of `25 = `1. We shall learn about sales tax with the help of the following examples. Example 18.1 The marked price of a suitcase is `850. The rate of sales tax is 6%. Find the amount paid by the customer to purchase the suitcase. Solution Marked price = `850 Sales tax levied = 6 \u00d7 850 = `51 100 Amount paid by the customer = `(850 + 51) = `901. Example 18.2 Sreekar purchases an article for `5200. If the rate of sales tax is 4%, find the marked price of the article. Solution Let the marked price of the article be `100x. Sales tax = 4% of 100x = `4x.","Sales Tax and Cost of Living Index 18.3 Total selling price of the article = `104x. Given that 104x = 5200 x = 50. \u2234 Marked price = 100x = 100 \u00d7 50 = `5000. Example 18.3 Calculate the total sales tax levied on the following products. (a)\t A cell phone worth `6000, sales tax at 8%. (b)\t An electric lamp worth `300, sales tax at 6%. (c)\t Readymade shirts worth `1500, sales tax at 8%. Solution Sales tax on the given commodities: Cell phone = 8 \u00d7 6000 = `480 100 Electric lamp = 6 \u00d7 300 = `18 100 Readymade shirts = 8 \u00d7 1500 = `120 100 \\\\ Total sales tax levied = `(480 + 18 + 120) = `618. Example 18.4 A customer goes to a store to buy a bag costing `648 at marked price. The sales tax to be levied on the bag is 8%. But the customer asks the trader to give a discount, after which she has to pay `648 to buy the bag. How much discount was given to the customer? Solution Let the price of the bag after the discount be `100x. Price after sales tax = 100x + 8x \t = `108x Given that 108x = 648 \u21d2x=6 Price after discount = `100x \t = 100 \u00d7 6 \t = `600 \u2234 Discount given = 648 - 600 = `48. Cost of Living Index An index is a relative number which indicates changes in prices of commodities, agricultural production, industrial production, cost of living, etc., over a certain period of time. The changes are marked with reference to a particular year. The year is called a \u2018base year\u2019.","18.4 Chapter 18 If the index number of agricultural production in April 2007 with reference to April 2006 (base year) is 105, it means that there is a 5% increase in the agricultural production from April 2006 to April 2007. Some of the index numbers that are commonly used are price index number, quality index number and cost of living index number. Though there are many index numbers that are commonly used, we focus on the cost of living index. We follow the weighted average method to find the cost of living index. In this method, the quantities of commodities consumed by a group of people are taken equal in number in both the years. These are considered as weights. The total expenditures for both the years are calculated. The year, for which the cost of living index is calculated, is referred to as the current year. Cost of living index = Total expenditure in the current year \u00d7 100 Total expenditure in the base year This method of finding the cost of living index can be better understood with the help of the following example. Example 18.5 Calculate the cost of living index for the year 2006 taking 1990 as the base year from the following information using weighted average method. Rate (in ` per kg) Commodity Quantity Consumed (kg) 1990 2006 Wheat 15 12 18 Rice 20 Oil 5 13 20 Gram 3 Sugar 5 30 50 30 60 12 18 Total price in the year 1990, for: Wheat = 15 \u00d7 12 = `180 Rice = 20 \u00d7 13 = `260 Oil = 5 \u00d7 30 = `150 Gram = 3 \u00d7 30 = `90 Sugar = 5 \u00d7 12 = `60 Total expenditure = 180 + 260 + 150 + 90 + 60 = `740 Similarly, total expenditure in 2006, for: Wheat = 15 \u00d7 18 = `270 Rice = 20 \u00d7 20 = `400 Oil = 5 \u00d7 50 = `250 Gram = 3 \u00d7 60 = `180 Sugar = 5 \u00d7 18 = `90 Total expenditure = `1190 \\\\\u2009Cost of living index in 2006 = Total expenditure in the year 2006 \u00d7 100 = 1190 \u00d7 100 = 160.8. Total expenditure in the year 1990 740","Sales Tax and Cost of Living Index 18.5 Example 18.6 Cost (in `\/kg) Item Quantity Consumed In 2007 In 2008 P 16 Y 50 Q y 20 32 R 10 24 y + 16 S 12 45 75 The cost of the living index for 2008, taking 2007 as the base year, is 200. Find y. (a) 10\t (b) 12\t (c) 14\t (d) 8 Solution Total expenditure in 2007 (in `) = (16)(y) + (y)(20) + (10)(24) + (12)(45) = 36y + 780 Total expenditure in 2008 (in `) = (16)(50) + (y)(32) + (10)(y + 16) + (12)(75) = 1860 + 42y 200 = 1860 + 42y \u00d7 (100) 36y + 780 2(36y + 780) = 1860 + 42y 30y = 300 \u2234 y = 10.","18.6 Chapter 18 TEST YOUR CONCEPTS Very Short Answer Type Questions \t1.\t The tax which is imposed on the sale price of an \t9.\t Akhila visits a readymade garment shop and pur- article is called _____. chases a top for `300, sales tax @ 3%. Calculate the total amount paid by Akhila to the shopkeeper. \t2.\t The _____ differs from item to item and state to state. (sales tax\/income tax) \t10.\t Index number measure relative changes in indus- trial production, agricultural production and also \t3.\t If the list price of an article is `50 and the rate in our _____ of living. of sales tax is 2%, then its selling price after tax is _____. \t11.\t The year for which we calculate the cost of living index is referred as _____ year. \t4.\t Calculate the amount paid by a customer for an article, if its list price is `1250 and the rate of sales 1\t 2.\t Rakesh purchased a shirt for `560 including sales tax is 5%. tax. Find the rate of sales tax if its list price is `500. \t5.\t Sales tax is calculated on the list price, if no _____ \t13.\t Aryan purchased a Plasma TV for `92,000 includ- is given. ing sales tax. Find the list price of the TV, if its sales tax is 15%. \t6.\t Sales tax is calculated on the _____ price, if \u00addiscount is given. \t14.\t Akhila visits a readymade garment shop and pur- chases a trouser for `800, sales tax @ 4%. Calculate \t7.\t The sales tax given will reach the _____. the total amount paid by Akhila to the shopkeeper. (shopkeeper\/government) 1\t 5.\t If the index number of sales prices in March 2006 \t8.\t The three index numbers which are commonly compared to March 2005 is 124, there is an increase used are _____, _____ and _____. of _____ in the wholesale price from March 2005 to March 2006. PRACTICE QUESTIONS Short Answer Type Questions \t16.\t The cost of living index in the year 2006, tak- 1\t 8.\t The reference year with respect to which we ing 2004 as the base year, on certain commodi- measure the changes in the current year is called ties is 162.75. If the total expenditure in 2004 was _____. `12,500, then find the total cost for the same com- modities in the year 2006. 1\t 9.\t Cost of living index = _____. 1\t 7.\t Akhila visits a readymade garment shop and purchases \t20.\t If the cost of living index of a certain year is 180 a jean jacket for `600, sales tax @ 5%. Calculate the and the expenditure in the current year is `36,000, total amount paid by Akhila to the shopkeeper. then the expenditure in the base year is _____. Essay Type Questions 2\t 1.\t If the total expenditures in the base year and cur- price such that she has to pay `44,240 including rent year are equal, then its index number is _____. sales tax. Find the discount needed on the price. \t22.\t Ganga visits a shopping mall to buy a necklace 2\t 3.\t Calculate the cost of living index for the year 2002, taking 1994 as the base year. Use weighted average costing `42,000. The rate of sales tax is 12%. She method. asks the shopkeeper to allow a discount on the","Sales Tax and Cost of Living Index 18.7 Price per Price Price unit in (`) in in Quantity 1994 2002 Quantity 2002 2006 Consumed 18 24 Commodity Consumed (`) (`) Commodity (in units) 11 16 A 18 12 20 Rice 85 kg 10.00 16.00 B 22 4 10 per kg per kg C 13 45 80 Pulses 30 kg D 10 20 45 14.00 20.00 E6 Sugar 40 kg per kg per kg F5 Coffee 8 kg 12.00 15.00 per kg per kg \t24.\t Shilpa purchases a refrigerator having a list price of Oil 20 litres `10,500 at 12% discount. If sales tax is charged @ 120.00 140.00 5%, then find the amount Shilpa has to pay to the Cylinder 4 per kg per kg shopkeeper. 40.00 60.00 \t25.\t From the following data, using weighted average per litre per litre method, calculate the cost of living index for the year 2006, taking 2002 as the base year. 200.00 350.00 per per filling filling CONCEPT APPLICATION Level 1 \t1.\t A shopkeeper sells an article, whose cost price is \t\t(a) `43,200\t\t (b) `48,000 `400, for `462 including sales tax @ 5%. Find the profit percentage of the shopkeeper. \t\t(c) `24,000\t\t (d) `28,000 \t\t(a) 7%\t\t (b) 12% \t5.\t If the index number of wholesale prices in May PRACTICE QUESTIONS 2004 as compared to May 2003 is 91, then the \t\t(c) 10%\t\t (d) 8% expenditure in the year 2004 is less by _____. \t2.\t Varshit purchased a pair of shoes for `3360 includ- \t\t(a) 8%\t\t (b) 7% ing a VAT of 12%. Find the amount he paid towards VAT. \t\t(c) 9%\t\t (d) 10% \t\t(a) `240\t\t (b) `360 \t6.\t A shopkeeper sells an article, whose cost price is `500, for `616 including a sales tax @ x%, and for \t\t(c) `300\t\t (d) `410 a profit of `50. Find x. \t3.\t Nalini purchases a bicycle for `2093 inclusive of \t\t(a) 8%\t\t (b) 10% sales tax @ 15%. Find its list price. \t\t(c) 12%\t\t (d) 9% \t\t(a) `1802\t\t (b) `1820 \t7.\t The cost of living index in 2007, taking 2006 as the \t\t(c) `1280\t\t (d) `1208 base year, is 175. The total expenditures in 2006 and 2007 are `(4x + y) and `(3x + 4y) respectively, \t4.\t On certain consumable goods, the total expendi- where x and y are integers. Which of the following ture of a family was found to be `18,000 in the can be the total expenditure of 2007? year 2005. If the cost of living index for the year 2006, taking 2005 as the base year, is 240, then \t\t(a) `48,000\t\t (b) `39,000 find the expenditure of the family on the same quantity of consumable items in the year 2006. \t\t(c) `43,000\t\t (d) `45,500","18.8 Chapter 18 \t8.\t Dheeraj bought a watch whose list price is `6500. 12. The shopkeeper allowed a discount of 6%, and asked to pay 10% VAT. Find the amount that Cost per kg Dheeraj paid for buying the watch. (in `) \t\t(a) `6481\t\t (b) `6625 Item Quantity In In Rice Consumed (kg) 2001 2007 \t\t(c) `6721\t\t (d) `6845 Jawar Wheat 80 15 18 9.\t Vegetables 35 20 24 Rate per kg (in `) Coffee 20 10 14 120 56 Quantity In the In the 10 50 80 (in kg) Year Year Item 12 2000 2007 \t\tFind the cost of living index in the year 2007, tak- A x ing 2001 as the base year, based on the information B 8 X 50 given above. C D 10 16 31 \t\t(a) 127.50\t\t (b) 128.75 20 x + 20 \t\t(c) 132.50\t\t (d) 135.25 86 40 \t\tThe cost of living index for the year 2007 consid- 1\t 3.\t In the year 1980, the total expenditure of a family ering the base year as 2000, is 225. Find x. was `8400. The cost of living index for the year 1980, by taking 1940 as the base year, was 240. \t\t(a) 15\t\t (b) 18 Then the expenditure of the family in the year 1940 was _____. \t\t(c) 12\t\t (d) 20 1\t 0.\t The total expenditure of a certain family was \t\t(a) `3000\t\t (b) `3500 `13,090 in the year 2000. If the cost of living index in the year 2006, when compared to the cost in the \t\t(c) `3800\t\t (d) `4200 year 2000, is 120, then the total expenditure in the PRACTICE QUESTIONS current year is _____. (in `) 1\t 4.\t The ratio of the total expenditure for the years 2000 and 2006 is 5 : 8. The cost of living index of 2006, taking 2000 as the base year, is _____. \t\t(a) 14,280\t\t (b) 15,240 \t\t(a) 125\t\t (b) 62.5 \t\t(c) 16,840\t\t (d) 15,708 \t\t(c) 160\t\t (d) Cannot be determined 1\t 1.\t Vikram purchased a TV for `13,500 including 1\t 5.\t When the year 2000 is taken as the base year, the sales tax. If the rate of sales tax is 8%, then the list cost of living index is increased by 20% from 2006 price of the TV is _____. (in `) to 2007. If the total expenditure in the base year is `20,000, and the cost of living index of 2007 is \t\t(a) 13,100 210, then the total expenditures (in `) in the years 2006 and 2007 are_____. \t\t(b) 12,800 \t\t(a) 35,000, 42,000\t (b) 30,000, 40,000 \t\t(c) 12,500 \t\t(c) 35,000, 45,000\t (d) 30,000, 42,000 \t\t(d) 11,950 Level 2 e\u00adssential commodities is `35,000. What is the amount he spent in the year 2007 towards essential \t16.\t The cost of living index of the year 2007, when commodities, if the quantity of consumption in compared to year 2005, is 165.7. The cost of liv- both the years remains the same? ing index for these two years is calculated consid- ering the prices of certain essential commodities. The amount spent by Anil in year 2005 towards","Sales Tax and Cost of Living Index 18.9 \t\t(a) `37,762\t\t (b) `48,719 \t\t(i)\tA double cot bed listed at `8360, sales tax @ \t\t(c) `57,995\t\t (d) `46,750 10%. 17. \t\t(ii)\tA wardrobe listed at `8650, sales tax @ 8%. Rate per kg \t\t(iii)\tA TV stand listed at `500, sales tax @ 9%. (in `) \t\tFind the total tax paid by Rohit on the above pur- Quantity chases. (in `) (in kg) Item 105 In 2000 In 2007 \t\t(a) 1483\t\t (b) 1523 A 14 20 B 15 12 X \t\t(c) 1653\t\t (d) 1573 C 10 20 D 27 5 10 \t22.\t Alok bought a scientific calculator for `728, including sales tax. The list price of the calculator 36 was `650. Find the rate of sales tax. \t\tThe cost of living index for the year 2007, consid- \t\t(a) 9%\t\t (b) 10% ering the year 2000 as the base year, is 250. Find x. \t\t(a) 167\t\t (b) 158 \t\t(c) 11%\t\t (d) 12% \t\t(c) 150\t\t (d) 162 2\t 3.\t A furniture set was listed at `62,400. It was sold at 20% discount. The sales tax charged on it was 1\t 8.\t Sujit purchased a furniture set which is listed at 10%. Find the amount to be paid to purchase the `58,600 followed by a discount of 10%. If sales tax furniture. (in `) is charged at the rate of 5%, then the amount Sujit has to pay to buy the furniture is ____. (in `) \t\t(a) 54,912\t\t (b) 57,408 \t\t(a) 53,477\t\t (b) 55,377 \t\t(c) 52,416\t\t (d) 49,920 \t\t(c) 56,446\t\t (d) 54,658 2\t 4.\t Pavan went to a mobile phone store. He wanted \t19.\t Ananya goes to a store to buy a mobile phone to buy a mobile phone listed at `6075. The rate of costing `15,675. The rate of sales tax is 10%. She asks the store keeper to allow a discount to such an sales tax was 11 1 %. He requested the shopkeeper extent that she has to pay `15,675 inclusive of sales 9 tax. Find the amount of discount to be allowed by to give a discount such that he only needed to pay PRACTICE QUESTIONS the shopkeeper. `6075 including sales tax. Find the discount Pavan \t\t(a) `1220\t\t (b) `1567 must be given to fulfill his request. (in `) \t\t(c) `1375\t\t (d) `1425 \t\t(a) 607.50\t\t (b) 596.50 \t\t(c) 580.50\t\t (d) 616.50 2\t 0.\t Rishi purchased a scientific calculator for `736, 2\t 5.\t The price of a TV, inclusive of sales tax of 12%, is including sales tax. If the list price of the calculator `15,680. If the sales tax rate is increased to 14%, is `640, the rate of sales tax is ______. then what additional amount of money a customer should pay for it? (in `). \t\t(a) 12%\t\t (b) 15% \t\t(c) 18%\t\t (d) 20% \t\t(a) 280\t\t (b) 240 \t21.\t Rohit went to a shop and purchased the following \t\t(c) 260\t\t (d) 300 goods. Level 3 2\t 6.\t The price of a washing machine, inclusive of sales \t\t(a) `175\t\t (b) `240 tax at 11%, is `5550. If sales tax is increased to 13%, \t\t(c) `100\t\t (d) `650 then what amount of additional money a customer should pay to buy it.","18.10 Chapter 18 \t27.\t Three essential commodities, the quantities of \t\tFind the amount of tax paid by Anshu on these their consumption and their prices in the years goods. 2000 and 2007 are listed below. The cost of living index for the years 2000 and 2007 is calculated on \t\t(a) `479.50\t\t (b) `384.50 the prices of these three commodities only. \t\t(c) `345.00\t\t (d) `493.00 2006 2007 \t31.\t Ashok sold an article, whose cost price is `300, for `351 including sales tax @ 8%. Find his profit Consumption Price\/ Consumption Price\/ percentage. Commodity (in kg) kg (in kg) kg A xy 2x y \t\t(a) 13 1 % \t\t (b) 8 1 % 3 3 B yz y 2 4z 2 2 16 3 % 10 3 % C z x 2z x \t\t(c) \t\t (d) \t\tFind the cost of living index of the year 2007, tak- \t32.\t Arun bought a motorbike at a discount of 10%, ing 2006 as the base year. and paid a sales tax @ 8%. He paid it for `47,142. Find its list price. (in `) \t\t(a) 200\t\t (b) 100 \t\t(c) 150\t\t (d) 50 \t\t(a) 48,500\t\t (b) 49,500 2\t 8.\t Ritesh went to a shopping mall to buy a trouser \t\t(c) 50,500\t\t (d) 51,500 costing `3500. On his request, the shopkeeper allowed two successive discounts of x% and y% (x 3\t 3.\t A shopkeeper sold an article, costing `360, for > y). If Ritesh paid `2618 including sales tax of `495 including a sales tax of y% at a profit of `90. 10%, then which of the following could be the Find y. discount rates given by the shopkeeper? \t\t(a) 8\t\t (b) 12.5 \t\t(a) 20%, 15%\t (b) 20%, 10% \t\t(c) 15\t\t (d) 10 \t\t(c) 20%, 25%\t (d) 15%, 10% 3\t 4.\t The ratio of the total expenditures of a family for the years 2002 and 2007 is 4 : 7. Find the cost of living PRACTICE QUESTIONS 2\t 9.\t On certain consumable commodities, the total index for the year 2007, taking 2002 as the base year. expenditure of a family was found to be `28,000 in the year 1994. If the cost of living index for the \t\t(a) 135\t\t (b) 155 year 2000, taking 1994 as the base year, is 265, then the expenditure of the family, on the same \t\t(c) 175\t\t (d) 195 quantities of consumable commodities, in the year 2000 is _____. 3\t 5.\t The cost of living index of the year 2006, taking the year 2005 as the base year, is 225. The total \t\t(a) `78,000\t\t (b) `79,000 expenditures in 2005 and 2006 are `(2x + 7y) and `(7x + y) respectively, where x and y are positive \t\t(c) `78,200\t\t (d) `74,200 integers. Which of the following can be the total expenditure in 2005? (in `) \t30.\t Anshu visits a super market and purchases the fol- lowing goods: \t\t(a) 37,600\t\t (b) 47,600 \t\t(A) A\u0007 dinner set which is listed at `1750, sales tax \t\t(c) 28,400\t\t (d) 27,200 @ 5%. \t36.\t The total expenditure of a family 2003 was \t\t(B) A\u0007 computer table, for `2700 including sales tax `15,000. Taking this year as the base year, the cost @ 8%. of living index in 2007 and 2008 were calculated. The cost of living index 2008 was 25% more than \t\t(C) A\u0007 bag of rice which is listed at `4800, sales tax that in 2007. The cost of living index in 2008 was @ 4%.","Sales Tax and Cost of Living Index 18.11 160. Find the total expenditure of the family in of VAT is 15%, then find the amount that Ramesh 2007. (in `) paid for the book. (in `) \t\t(a) 17,500\t\t (b) 18,000 \t\t(a) 793.50\t\t (b) 767.50 \t\t(c) 805.50\t\t (d) 813.50 \t\t(c) 18,400\t\t (d) 19,200 3\t 7.\t Ravi bought a pair of slippers for `944, including a \t39.\t The list price of an AC is `20,000. The shopkeeper VAT of 18%. Find amount of VAT he paid. (in `) sold it by allowing a 4% discount and charged 5% sales tax. By mistake, while calculating the bill, \t\t(a) 108\t\t (b) 132 he considered 5% discount and 4% sales tax. As a result, the customer must have paid ______. \t\t(c) 144\t\t (d) 128 3\t 8.\t Ramesh bought a book whose list price is `750. \t\t(a) `200 less\t (b) `400 less The shopkeeper gave him 8% discount. If the rate \t\t(c) `400 more\t (d) `200 more PRACTICE QUESTIONS","18.12 Chapter 18 TEST YOUR CONCEPTS Very Short Answer Type Questions \t1.\t sales tax \t9.\t `309\t \t2.\t sales tax 1\t 0.\t cost \t3.\t `51\t \t11.\t current year\t \t4.\t `1312.50 \t12.\t 12% \t5.\t discount\t 1\t 3.\t `80,000\t \t6.\t selling 1\t 4.\t `832 \t7.\t government\t 1\t 5.\t 24% \t8.\t price index number, quality index number and cost of living index number. Short Answer Type Questions 19.\t Total expenditure in the current year \u00d7 100 Total expenditure in the base year \t16.\t `20,343.75\t 1\t 7.\t `630 \t20.\t `20,000 \t18.\t Base year Essay Type Questions 2\t 4.\t `9702 2\t 5.\t 145.70 \t21.\t 100\t \t22.\t `2500 2\t 3.\t 163.34\t ANSWER KEYS CONCEPT APPLICATION 5. (c)\t 6. (c)\t 7. (d)\t 8. (c)\t 9. (a)\t 10. (d) 15. (a) Level 1 \t1. (c)\t 2. (b)\t 3. (b)\t 4. (a)\t \t11. (c)\t 12. (a)\t 13. (b)\t 14. (c)\t Level 2 18. (b)\t 19. (d)\t 20. (b)\t 21. (d)\t 22. (d)\t 23. (a)\t 24. (a)\t 25. (a) \t16. (c)\t 17. (c)\t Level 3 28. (a)\t 29. (d)\t 30. (a)\t 31. (b)\t 32. (a)\t 33. (d)\t 34. (c)\t 35. (a) 38. (a)\t 39. (b) \t26. (c)\t 27. (a)\t \t36. (d)\t 37. (c)"]