Math5

Example 2: A square field has a side of 19.2 m. Find its perimeter. Side ofthe square field = 19.2 m Therefore, the perimeter I of the square field = 4 x side 19.2 m = 4x19.2m = 76.8 m Thus, the perimeter of the square field is 76.8 m. <--19.2m-------------> I Example 3: Find the side of a square whose perimeter is 32 cm. Perimeterofthe square = 4 x side 32 cm = 4 x side lciven that perimeter is 32 cm] Therefore, side = #4cm = 8cm Thus, the side of the square is 8 cm. .fr|5T 1. Find the perimeter of the following figures. 'I.1' 1b I 15 cm 20 cm I +20cm+ I <- 10 m --> <-25€m----------------> 1' 1 83 cm 28 cm 1\" I + I28cm-----------> <- 162 cm ---------------'' + I 28cm+ 2. Find the perimeter of the following squares and rectangles. a. length = 15 cm, breadth = 12 cm b. side = 12 cm c. length = 2.6 m, breadth = 1.3 m d. length = L2 m, breadth = 9 m

side=2m f. length = 58 cm, breadth = 32 cm side = 25 cm h. length = 5 m, breadth =7 m side = 4.8 m j. length =8 cm, breadth =5cm K. length = 54 cm, breadth = 54 cm l. side = 66 m 3. Find the side of the square, whose perimeter is given below: a. P=40cm b. P=24m c. P=4.8m d. P=120cm e. P=23.6m 4. The length of a carpet is 3.4 m and the breadth is 2.3 m. What will be its perimeter? nd the perim ete r of the given figures. t b. 1 18.9 m I +_22.5m+ I 44.9 cm I + +44.9 cm * Area The amount of surface occupied by a closed figure is called its area. In your earlier class, you have learnt how to find the area of a figure using a square grid. But this process is only applicable for measuring smaller areas as it is not possible to count the number of square grids for measuring larger areas. So, let us develop formulae for finding the area of simple geometrical figures. Area of a Rectangle Ramva went to an auditorium with her father. There she found that the floor has tiles whose each side is of 1 m. She became curious to find the area of the floor Ramya : Papa! Can you tell me the area of the floor without counting all the tiles? Papa Yes. lt is 216 so. m. Ramya How did you find that without counting all the tiles? Papa That is very simple ! Count the number of tiles along the length of the floor, which is 18. Since the length of each tile is 1 m, so the length of the floor is 1.8 m. Similarly, count the number of tiles along the breadth, which is 12. 50, the breadth of the floor is 12 m. Multiply the length and the breadth. The result is 216 sq. m, which is the area of the floor. DI<_ B Do not forget to write the unit. Thus, it can be inferred from above that t _Area of a rectangle = / x, = l-ength x Breadth b .II\\Jtg42ltfTtr----- rv t------------>C

Example 1: Find the area ofa rectangle whose length is 43 cm and breadth is 32 cm. cmtength ofthe rectangle = 43 K L Breadth ofthe rectangle = 32 cm t Therefore, area ofthe rectangle = 43 cm x 32 cm 32 cm = 1376 sq. cm + N <__43cm_>M Thus, the area of the rectangle is 1376 sq. cm. Example 2: A rectangular plot has an area of 103.70 sq. m. tts breadth is 8.5 m. Find its length. Area ofthe plot = 103.70 sq. m +/___> 1 Breadth of the plot = 8.5 m 8.5 m A = 103.70 sq. m Area of the plot = Length x Breadth I 103.70 sq. m = Length x 8.5 m Therefore, length of the ptot = 1_r9! rn = rZ.z 1r1 Thus, the length of the plot is 12.2 m. Area of a Square A square is a special rectangle whose length is equal to its breadth. Therefore, the area of a square = length x breadth = JX,' Thus, area of a square =sxs= side x side D<- s +C Example 1: What is the area of a wall whose each side measures 6 m? I Side of the wall = 6 m 6m Therefore, the area ofthe wall = side x side j = 6mx5m=36sq.m Thus, the area of the wall is 36 sq. m. 2:Example Find the area of a square scarf of side 55.5 cm. +6m- Side ofthe scarf = 55.5 cm Therefore, area ofthe scarf = side x side = 55.5 cm x 55.5 cm = 3080.25 sq. cm +55.5cm-+ Thus, the area of the scarf is 3090.25 sq. cm.

t <_-6.2m4 Example 3: Find the area of a photo frame whose each side measures 6.2 m' Side of the frame = 62m Therefore, area of the frame = 62mx62m = 38.44 sq. m Thus, the area of the photo frame is 38 44 sq' m' Units of Area Area is measured in square units' Smoller oreos ore 1. lf dimensions are in mm, unit of area will be meosured in sq. cm ond larger oreos sq. mm or mm'z sre meosured i4 2. lf dimensions are in cm, unit of area will be sq. cm or cm'. 3. lf dimensions are in m, unit of area will be sq m or m'' 4. lf dimensions are in km, unit of area will be sq' km or km'' 1. Find the area of the following rectangles/squares' a. length = 3 cm, breadth = 5 cm b. length = 3.1 cm, breadth = 2'8 cm c. side=8cm d. length = 5.8 m, breadth = J Z m e. side = 5.5 m I length = 12.1cm, breadth = 8'2 cm g. side = 6.3 cm h. length = 7.3 cm, breadth = 5'8 cm i. side = 76.5 cm j. length = 14.5 m, breadth = 4 m 2. Find the measure of the side of a square' if its area is d. 144 sq. m a. 36 sq. cm b. 49 sq. m c. 64 sq. cm : 3. What will be the area of a bed whose length is 4'7 m and breadth is 3 2 m? A Raunak painted two walls of a room The length and breadth of each wall is 7 5 m and +.+ m, respectively. Find the total area of the walls he painted' 5. Abdul wants to change the tiles of the floor of his room How many square tiles of side 1 unit will be needed if the length of the room the breadth is L8 units? is 25 units and

VE Shashank s class has two notice boards. One is a square of side 15S cm and are the the other is a rectangre of rength 110 cm and breadth 72 cm. what -- perimeters of the two boards? Which board will cover more area? One day Shashank got late while leaving the classroom and in his hurry to catch the school bus, his school bag accidentally hit the notice board and its glass door broke. Next day, he made confession and apologised to his class teacher and offered to reprace the this incident? grass door. what quarity oi shashant< is evident in bagA. Respect for teachers B. Respect for school C. Honestv According to you, what is the significance of the above said value? 1. Students plant trees along the edges of a rectangular garden. lf the area of the rectangular garden is 36 cmr, then find the possr:ble values of 2. length and breadth. For each pair, find the perimeter of the garden. lf the area of a square is 1OO sq. units, then what is its perimeter? Area of a Triangle Take a rectangurar coroured paper and cut it arong the dotted rine as shown. What do you get? The rectangle is equally divided inro two triansles. Can you find the area ofthe triangle? Since the triangle is half of the rectangle, its area will also be half the area of the rectangle. jTherefore, area of a triangle = x area of the rectangle Example 1: In the given fjgure, find the area of the triangle if area of each small rill 1sq. unit. liii square is Area of the rectangle = 7 x 4 = 2g sq. unjts Therefore, area of th-('Irlangle = )Q -sq.units = 14 sq. units Thus, the area of the triangle is 14 sq. units.

Example 2: In the given figure, find the area ofthe triangle if area of each small square 1sq. unit. is Area of the rectangle = 6x5=30sq.units Therefore, area of the triangle = 30 sq, unlts 2 1\"5 sq. units Thus, the area of the triangle is 15 sq. untrs. Find the area of the following triangles if each small square has a side ot 1 unlt. 1. 5. 4. Area of lrregular Shapes You are already familiar with the ldea of finding the area of an irregular shape. How to find the area of the given shape? The area of this shape can only be approximately estimated, and cannot be exactly calculated. Step 1: Place the shape on a L x l\" square grid.

Step 2: Count the number of complete unit Do not couni-o squares covered by the shape. square, if less ihon They are 24. holf squore is covered I Step 3: Count the number of unit squares which are by the shopel half or more than half covered by the shape. They are 10. lgnore the squares that are covered less than half. Step 4: Add allthe unit squares obtained in Step 2 and Step 3. 24+LO=34 Thus, the approximate area of the shape is 34 sq. units. Find the approximate area of the following figures, if the area of each small square is 1 so. unit. Torget Olympiod 1 L' ,/

t complete the given figures so that the area of Figure 1 is 8 sq units' Figure 2 is 21.5 sq. units and Figure 3 is 24 5 sq units' 2. Find the area of the shaded portions if the area of swimming pool' lawn' playground and car parking are the same' swimming Pool 1 50m 20m I Playground Car Parking + 30m + <- 30m - MY Proi\":t Measure the dimensions of your eraser, pencil box, set squares from Vour geometry box' a postcard and a stamp. Find their Perimeter and area. Record Your findings 12 cm The area of this rectangle is/x b = 12 x 8 = 96sq' cm' tt The diagonal (BD) divides the rectangle into two triangles of equal area. so what is the formula for finding the area of a traingle? i' ixa1 b\"t\", heieht = 12 x 8 = 48 sq. cm

Wo@G@ Solve the crossword puzzle by finding the perimeter for the clues given in Down and the area for the clues given in Across. (Note: units to be ignored for filling answers.) Down 1. Square of side 3L units 2. Rectangle of length 11.5 units and breadth LO units A Rectangle of length 38 units and breadth 34 units 5. 87 units 8. 25 units 240 units 100 units 32 units ACrOSS 190 units 3. 7 more than the area of a square of side 1.6 units 4. Rectangle of length 12 units and breadth 87 units 5. Rectangle of length 6 units and breadth 8 units 7. Square of side 80 units D[stssr[4D A-uIIUV Objective: To find area and perimeter of rectangles, squares and L-l triangles Materials required: Strings of length 12 cm, board pins, board, \\ ruleI pencil Method: 1. With a ruler, draw rectangles and squares of dimensions of your choice and find their area and perimeter using formulae. From the rectangles and squares, draw triangles and find their area too. 2. Take three strings each of length 12 cm. With the help of the strings and board pins, form rectangles, squares and triangles on a board. lvleasure their length and breadth and also find their area. Which figure has the maximum area? What are the lengths of its sides? Students can do this activity with different lengths of strings and record their observations.

i llilsg i 1. Find the area of the following figures. .t_I ___--1t1r uI.t-----lll^ c. ^|\\N---i -tdf-----1t Ir---------------- t:t ii |I ->I|l'IV!.\". | \\; I lr3t8cm i I l'i'' I *il \\il:; <-15 |\\r +52cm+ : <- 10 m -' cm i z. complete the following table. ia.b.c.de.fg.h.i.j' i llLeennegtth ((mm) ) | t 4 Ll 13 8 6 89 : lBBrreeaadtdht(hm()m) ls 24 42 9 : FP\"errim-\"ette\"r({\"mt) I !2 36 i laArreea l(sqo. mm) ) I 49 48 81 64 (square) i| | (square) (square) i3. Findtheareaof the following irregular shapes if theareaof eachsmall square i is 1sq. unit. ia.-b.c. i4. Find th\" length of a ribbon to be pasted around a picture of length 40 cm and : gg cm. Find the area ofthe picture also. i s. whut is the area of the glass needed to cover a photograph of length 35 cm : breadth 20 cm? i 6.: - What is the area of a wall of length 18 m and breadth 12 m-,)? A^ lrs-^o fai:n-,.d1 ii]t-s p^^e.ri6im, eter' i7.: How many square tiles of side 40 cm are needed to build i the floor of a room of length 16 m and breadth 10 m? ig. How many square metres of sun shield will be i required to cover two rectangular windows of length i r::.^^ i S and breadth 2 m and four square windows of stde z m!' F: OO OO , I lsol f -b,lG

Sachin and his friends wanted to make placards to cheer up the school,s football team in the Interschool Football Tournament. They designed the placards in white and red colours which are matching with the colours of the jersey of their football team. oo o o o oo o oo They decided to stick letters,,We Win,, on a white square placard whose side is 90 cm. The letters in \"WE WlN\" consists of only big and small rectangles of crepe paper whose uniform width is 1.5 cm. The length of each ofthe big rectangles is 1G cm and that of each of the small rectangres is 6 cm. They decided to stick a race a[ around the four sides of the square placard. 1. How much lace is needed to stick all around the square? 2. What is the area of the white base? 3. How much area of red crepe paper is needed to make the letters ,.WE WlN,,? 4. What is the difference between the total areas and perimeters ofthe big and small rectangles? F F ra E F r ; r E_tr.-4 A E F Ft.F_d-t!t:.!LEr,L!t___.f_.E !+{++!+{+++ ! ! ! !+F+FF[+!+ H.

to Volume Ahana went to a sweet shop with her mother to buy coshew borls. She saw the shopkeeper making a box from a cutout of cardboard. After reaching home, she emptiedthe coshew borJis into another vessel, opened the flaps of the box, made it flat and tried to maKe the box again. She then filled the box with laddoos. But some laddoos were left after filling in the box. Ahana Mama, there were !2 cashew barfis in this box before. WhV am I not abte to keep 12 laddoos now? Mama It is not the number that counts. lt is the space occupied by the objects that counts. Laddoos definitely occupy more space than barfis. Ahana Oh! I see. Mama The space occupied by an object is called its volume. Can you fill your water bottle with 10 litres of water? No, because your bottle cannot hold 10 litres of water or in other words, the volume of your bottle is less than -LU rres-

Moths Around Us Raj received many gifts on his birthday. He tried to open one of his gifts which was packed inside a box. He opened it and made the box into a flat cardboard. on seeins that, his mother told him that the flat cardboard was the net of the cuboidal box which he had opened. Also, that box contained five tetra packs of juace each having 200 mL of juice. Raj felt very happy to receive his gifts and also gained the knowledge about the shapes and their nets. Length, Breadth and Height The distance between two side faces of a cuboid is called its length. The distance between the front face and the back face is called its breadth. The distance between the top face and the bottom face is called its height. Length is denoted by /', breadth is denoted bv,b, and height is denoted bv 'ft,. We measure length in metre or m, area in m2 or sq. m and volume in m3 or cubic metre, that is, cu. m. Example: What is the volume of the given figure? The given figure consists of 10 unit cubes. Thus, its volume is 10 cubic units. Volume of Solid Shapes with Unit Cubes How to measure the volume of a box? To measure the volume of the box, fill it with small cubes of side 1 unit. Volume is measured in cubic units. A cube of side 1 unit occupies 1 cubic unit of volume or space. Suppose a box can hold 258 unit cubes. So, its volume will be 258 cubic units. Volume is measured in cubic millimetre or mm3, cubic centimetre or cm3 and cubic metre or m3.

Example 1: What is the volume of this solid, if the volume of each small cube is L cm3? Also find its length, breadth and height. The given solid consists of 9 unit cubes. Thus, its volume is 9 cubic units. From the figure, we can see that its length is 3 units, breadth is 1 unit and height is 3 units. Example 2: Find the volume ofthe given figure, considering the volume of each small cube as 1 cm3. The given figure consists of 1.2 unit cubes. Thus, its volume is 12 cubic units. 1. Find the length, breadth and height of the given figures. Also find their volume, if the volume of each small cube is L cm'. b. d. 2. Find the volume of the given figures where each small cube is of volume 1 cm3 a, b.

d. e. ) Volume of a Cuboid Suppose you are given a box of length 10 cm, breadth 5 cm and height 8 cm. lf you fill the box with small cubes of volume 1cm3, then how many cubes can you place along the length and along the breadth of the box? Here, 10 cubes can be placed along the length and 5 cubes along the breadth of the box. lf the entire base area is to be covered with the cubes, then how many cubes do you need? After counting, you can see that the entire base +1ocubes- ____> can be covered With 5 x 16 = 59 .uo\"t Now, can you find out how many layers of cubes are required to fill the box? Here, the answer is 8 layers, that is, the height of the cuboid. So, what is the total number of cubes? 8 x 50 = 400 cubes Therefore, the volume of the box is 400 cm3. Let us now multiply the length, breadth and height of the box. I x b x h = 10 cm x 5 cm x 8 cm = 400 cm3, which is nothing but the volume of the box. Thus, volume of a cuboid = length x breadth x height = / x, x /, Example 1: Find the volume of a cuboid of length 8 cm, breadth 2 cm and height 4 cm. Given, Length = 8 cm, Breadth = 2 cm and Height = 4 cm +8.m-- Volume = length x breadth x height =8cmx2cmx4cm=64cm3 Thus, volume of the cuboid is 64 cm3.

Example 2; Find the volume of the cuboid whose length is 12 m, breadth is L0 m and height is 9 m. Given, T Length = 12 m, Breadth = 10 m and Height = 9 m Volume = 12 m x 10 m x 9 m = 1O8O m3 +12m Thus, volume of the cuboid is 1080 m3. - Volume of a Cube A cube is a special type of cuboid whose length = breadth = height. That is, all the sides of a cube are individual squares. x,Therefore, volume of a cube = / x lr = (s x s x s,l cubic units, where s is the length of each side of the cube. Example 1: Find the volume ofthe following cubes. Il^. a. (]rven, srde = J cm 3cm Therefore, volume = 3 cm x 3 cm x 3 cm = 27 cm3 I b. Given, side = 8 m 3cm Therefore,volume = 8 m x 8 m x 8 m = 51.2 m3 Example 2: What will be the volume of a rubik cube of Volume side 5 m? of on object will hove some cubic unii os the Volume of the rubik cube = s x s x s = unit of its = stTl x5mx5m dimensions. = LZ> m' Thus, volume of the rubik cube is 125 m3. 1. Find the volume of the followine solids. a. ,t 6m +30m- <-15€m+

+v15.m 1 15 €m + // >vt./30 cm +20cm+ in the missing data. a. lf length =3 m, breadth = 3 m and height=2 m, thenvolume is D. lf the edge of a cube is 4 m, then its volume is ,c. lf I = 725 cm, b = 105 cm and volume = 13125 cm3, then is lf b = 12 cm, h = 4 cm and volume = 96 cm3, then / is e. lf volume is 8 m3, then edge of the cube is 3. A book is 30 cm long, 25 cm broad and 3 cm thick. What is the volume ofthe book? 4. A box has an equal length, breadth and height of 35 cm. What is its volume? 5. What is the length of the edge of a cube of volume 1OOO cm3? 6. The length and breadth of a fish tank are 50 cm each and its hejght is 40 cm. Find its volume. lVgl 'l memory of their grandparents, Mehak and Shirish distribute sweets in an Otd Age Home every year on their birthday. Mehak is packing sweets in a cubical box -. of side 60 cm and Shirish is packing sweets in a cuboidal box of length G5 cm, breadth 40 cm and height 25 cm. Whose box will hold more sweets? What quality does this act of Mehak and Shirish deDict? a. Obedience b. Love and respect for elders c. Empathy t. A wall of length 50 m and height t 0 m is to be built. One_tenth of its volume is cemeftt and the rest are bricks. Find the volume of the bricrs used in it if the breadth of the wall is 2 m? 2. Two-thirds of the height of a cubical fish tank is filled with water. tf the length of the tank is 60 cm, breadth is 30 cm and height is 45 cm, then find the volume of the unfilled portion of the tank.

Nets What do you usually do with a gift box after taking out the gift from it? Throw it away. lsn't it? Next time, open its flaps till it is flat from all the sides. This flat shape obtained is called a net. Net of a Cube All the sides of a cube are squares. lf you fold the net on the left hand side along the dotted lines, you will get an open cube. lf you fold the net on the right hand side along the dotted lines, you will get a closed cube. Net of a Cuboid Sides of a cuboid are rectangular in shape. Here is the net of a cuboid. lf you fold it along the dotted lines, you will get a closed cuboid. Can you think of some other nets of a cube and a cuboid? How many squares are there in the net of a cube and how many rectangles are there in the net of a cuboid? Net of a Cone The net of a cone will look like this. l'r Net of a Cylinder H The net of a cylinder will have a rectangle and two circles. L=TV A sphere does not have a net. -b,lt- -

Drawing Cubes and Cuboids You can draw cubes and cuboids on dotted sheets. There are two types of dotted sheets. 2. lsometric dotted sheet L. Ordinary dotted sheet An ordinary dotted sheet has dots which are aligned horizontally and vertically with one a nother. There is also a special dotted sheet called isometric dotted sheet on which vou can clearlv visualise all the sides of a solid shape. Drawing a Cube Below is a cube drawn on an ordinary dotted sheet and an isometric dotted sheet. Ordinary dotted sheet lsometric dotted sheet Drawing a Cuboid Below is a cuboid drawn on an ordinary dotted sheet and an isometric dotted sheet. Ordinary dotted sheet lsometric dotted sheet

1,. Draw the nets of the following shapes. h 2. Complete the following cubes or cuboids. a. b. e. f. Target Olympiod 1. A tank full of water has a square base and its height is half of its length. When some pebbles are dropped into it, + of the water flows out. tf the volume of the water that flows out is 8000 cm3, then find the dimensions of the tanK. 2. Volumes of a given cube and a cuboid are equal. The length of the cuboid is twice the length of the cube and the breadth of the cuboid is half the length of the cube. Find the height of the cuboid.

D[asug llnn #il Tfln Objective: To draw the front view'side view and top view of different shapes. Materials required: 20 to 30 blocks and pencil Method: Collect blocks and pile them one over the other to form a shape. Let us now draw its side view front view and top view Side view Front view Top view Repeat this with other shapes. NoW try to make different shapes using dice and draw their front, side and top views. My Proiect L t d_#..-_ create your own measuring glass Take some water in a glass and mark the level of water as '0'. Drop 5 marbles in it and mark the new level of water as 5 marbles. Keep on adding 5 marbles each time and create your markings on the measuring glass till 40 marbles. Now find the volume (in terms of marbles) of a ball, eraser, pencil, lemon and paper weight by dropping them in the glass when the water is at measure level 0. Note the change in the level of water and create an observation table.

Draw the front view side view and top view ofthe following figures and also find their volumes. b. c. _] Which of these nets can be made into cubes or cuboids? a. D. Find the volume of cube or cuboid with the following dimensions. a. I =2cm b. s= 25 cm c. I = 2Um d. s=45 m 6=3cm s=25cm D=30m s=45m h=Lcm s=25cm h=12m s=45m A room has a length of 12 m, breadth of 14 m and height of 3 m. What will be the volume of air in the room? A water tank has an equal length, breadth and height of 2 m each. What will be its volume? A box has a length of 42 cm, breadth of 35 cm and a heieht of 8 cm. What will be its volume? A chess board has an equal length and breadth of 55 cm each. Its height is 5 cm. What will be its volume?

Mr' Malhotrat famiry is going.for a horiday trip to shimra. Mr. Marhotra firmry berieves in \"self help is the best help,, and he, therefore, tells his wife, son and daughter that they must carry their own bags during the trip. He gives each one of them a bag in the shape of a cuboid of length 45 cm, breadth 30 cm and height 20 cm and tells them to pack whatever they want in that bag only. 1.. What is the volume of the given bag? 2. Each set of Rahult clothes occupies a space of 15OO cm3. He wants to carrv 8 sets of clothes and his camera box which is a cube of edge 20 cm. Will the bas be enough for him? 3. Mrs Malhotra wants to carry her bangles box whose length is 30 cm, breadth is L2 cm, and height is G cm along with the sarees sets. Each saree set occupies a volume of 1200 cm3. How many sets of sarees will she be able to carrv? 4. Rahul's sister Rajani wants to carry two extra sandals apart from her dresses. lf her dresses occupy the same vorume as Rahurs dresses, wi she be abre to carrv ten dresses and sandals if her sandals occupy a volume of 600 cm3 each? 5. Mr Malhotra wants to keep his laptop inside the bag which will occupy a volume of 12000 cm3. Will he be able to carry g sets of clothes if each set occuptes a volume of 2000 cm3?

Write a.m. or p.m. as applicable. a. /IRr\"r\\iNJ \\\\--6_11-,/ 3:00 in the 5:00 in the 12:30 in the 10:00 at night morning evening afternoon ConverL the tollowing into 24 hour clock time. a. 9:30 a.m: b. 12 noon: c. 8:15 p.m: o. 11:20 p.m: 6:1\"0 a.m: i 5:10 a.m: 9:43 a.m: n. 8:05 p.m: i. l.:25 p.m: Circle the leap years. 1998, L996, 7950,2004, 20t0, t942, 7912,2032 Name the months that have 3L davs. Convert the {ollowing into l2-hour clock time. a. zs:uu nours: b. 00:00 hours: c. 13:20 hours: d. 20:10 hours:

6. A movie starts at 6:30 p.m. and its total duration is 3 hours. At what time does the movie get over? 7. lf 18th May is a Sunday, then which day will fall on 5th September of the same year? 8. Ragini went on a foreign trip on r.sth october and returned on 29th october ofthe same year. Find the total number of days spent on the trip. 9. lf a competitive exam starts at 9:oo a.m. and gets over at r.1:oo a.m., then find the total duration of the examination. we already know that time is expressed either in 12-hour crock format or in 24-hour crock format. We also know that, L hour = 60 minutes 1 minute = 60 seconds l year = 365 days (366 days in case of leap year) Lweek = Tdays L day = 24 6ourt Converting Days into Hours To convert days into hours, multiply the number of days by 24. Example 1: Convert 6 days into hours. We know that, l day = 24 6orrt Therefore,6 days = 6 x 24 hours = 144 hours Thus, 6 days is equal to 144 hours. Example 2: Convert L1 days g hours into hours. We know that, l day = 24 6orr. Therefore, 11 days 8 hours = 1.1 x 24 hours + 8 hours = 264 hours + 8 hours = 272 hours Thus, 11 days 8 hours is equal to 272 hours. Converting Hours into Minutes To convert hours into minutes, multiply the number of hours by 60. Example 1: Convert 6 hours into minutes. We know that, t hour = 60 minutes Therefore,6 hours = 5 x 60 minutes = 360 minutes Thus, 6 hours is equal to 360 minutes.

Example 2: Convert 15 hours 34 minutes into minutes. We know that, t hour = 60 minutes Therefore, 15 hours 34 minutes = 15 x 60 minutes + 34 minutes . = 900 minutes + 34 minutes = 934 minutes Thus, 1.5 hours 34 minutes is equatto 934 minutes. Converting Minutes into Seconds To convert minutes into seconds, multiply the number of minutes bv 60. Example 1: Convert 25 minutes into seconds. We know that, 1 minute = 60 seconds Therefore, 25 minutes = 25 x 60 seconds = 15OO seconds Thus, 25 minutes is equal to 15OO seconds. Example 2: Convert 55 minutes 34 seconds into seconds. We know that, 1 minute = 60 seconds Therefore,55 minutes 34 seconds = 55 x 60 seconds + 34 seconds = 3300 seconds + 34 seconds = 3334 seconds Thus, 55 minutes 34 seconds is equal to 3334 seconds. Example 3: Convert 57 minutes 59 seconds into seconds. We know that, L minute = 60 seconds Therefore, 57 minutes 5g seconds = 57 x GO seconds + 5g seconds = 3478 seconds Thus, 57 minutes 58 seconds is equal to 347g seconds. 1. Convert into hours. b. 14 days c. 35 days e. 22 days 8 hours f. 41 days 12 hours a. 9 days h. 67 days 18 hours i. 78 days d. 55 days k. 58 days 17 hours l. 79 days 8 hours g. 49 days 20 hours j. 80 days lL hours

2. Convert into minutes. D. Z/ nOUrS c. 33 hours I 50 hours 12 minutes a. 12 hours e. 39 hours 6 minutes i. 36 hours 40 minutes d. 51 hours h. 96 hours 42 minutes l. 150 hours g. 87 hours 55 minutes j. 77 hours 56 minutes K, lzz nours 55 mtnutes 3. Convert into seconds. a. 43 minutes b. 52 minutes c. 74 minutes f. 34 minutes 22 seconds d. 98 minutes e. L5 minutes 5 seconds i. 70 minutes r. 4zu mtnutes g. h.76 minutes 44 seconds 98 minutes 1 second j. k.98 minutes 39 seconds 120 minutes 4. Seema compieted her maths homework in 45 minutes 30 seconds. Express the time taken by her for completing her homework in seconds. 5. The running time ofa documentary movie is 2 hours 45 minutes. Express the duration of the movie in minutes. 6. A mason works for 8 hours 20 minutes. Convert the time spent into minutes. 7. Yash takes 122 minutes to reach his office. Express the time taken in seconds. 8. Students of class V went on an excursion for 15 days. Find the total duration of the excursion: a. in hours. b. in minutes. c. in seconds. Converting Hours into Days To convert hours into days, divide the number of hours by 24. 2 <-Days Example 1: Convert 48 hours into oavs. 24)4f- We know that, 24 hours = l day -48 Therefore, 48 hours -- (48 + 24) days 2 days Thus,48 hours is equal to 2 days.

Example 2: Convert 127 hours into days and hours. 24\\d5 <- Davs We know that, 24 hours = j. day - 120 Therefore, 127 hours = ,l27 + 24) days 7 <-Hours 5 days 7 hours Thus, L27 hours is equalto 5 days 7 hours. Converting Minutes into Hours To convert minutes into hours, divide the number of minutes by 60. 4 <- Hours Example 1: Convert 240 minutes into hours. ou ) z4u We know that, 60 minutes = t hour - 240 Therefore, 240 minutes = (240 + 60) hours = 4 hours 0 Thus, 240 minutes is equalto 4 nours. Example 2: Convert 320 minutes into hours and minutes. 5 <--Hours We know that, 60 minutes = t hour ov ) szu - 300 Therefore,32O minutes = (320 + 60) hours 20 <-- Minutes = 5 hours 20 minutes Thus,32O minutes is equal to 5 hours 20 minutes. Converting Seconds into Minutes To convert seconds into minutes, divide the number of seconds by 50. Example 1: Convert 360 seconds into minutes. . 6 <- Minutes We know that, 60 seconds = L minute 60 ) 360 Therefore, 360 seconds = (360 + Go) minutes - 360 = 6 minutes Thus, 360 seconds is equal to 6 minutes. Example 2: Convert 432 seconds into minutes and seconds. 7 <- Minutes We know that, 60 seconds = 1 minute 60 J432- . Therefore,432 seconds = (432 + 60) minutes - 420 = 7 minutes L2 seconds 12 <--Seconds Thus,432 seconds is equal to 7 minutes L2 seconds.

1. Convert the following into d.ays and hours. a. 62 hours b. 155 hours c. 243 hours e. 144 hours f. zl44 hours d. 302 hours h. 720 hours i. 392 hours g. 288 hours k. 245 hours l. 480 hours j. 410 hours c. 1.25 seconds 2. convert the following into minutes and seconds. f. 332 seconds i. 480 seconds 320 seconds b. 515 seconds l. 452 seconds d. 360 seconds e. 220 seconds c. 624 seconds h. 540 seconds c. 222 minutes J. 729 seconds k. 840 seconds f. 840 minutes i. 550 minutes 3. convert the followins into hours and minutes. t. /25 mtnures a. 162 minutes b. 98 minutes d. 155 minutes e. 300 minutes g. 202 minutes h. 480 minutes j. 546 minutes K. bb/ mtnures 4. What is 888 minutes in hours and minutes? 5. What is 585 hours in davs and hours? A car takes 654 seconds to go around a circular path. Convert the time taken by the car into minutes and seconds. Abdul takes 25 seconds to run 100 m and Venkatesh takes 32 seconds to run 100 m. lf both of them run for 2 km, then how much more time in minutes will Venkatesh take than Abdul? Finding Time Duration Calculating the Number of Hours Example 1: Rohan started for his office at 7:45 a.m. and reached after 2 hours 20 minutes. What time did he reach office?

fl,\"I To find the reaching time, add the starting time and the time taken to travet. Starting time = 7:45 a.m. Time taken to reach office = 2 hours 20 minutes Now to find the reaching time, add 7 hours 45 minutes and 2 hours 20 mrnures. Write minutes in'minutes column, hours in hours column and then add. Step 1: Add the minutes column 45 + 20 = 55 minutes @, =lhour5minutes 45 2 20 Regroup L hour to hours corumn and write 5 minutes in minutes column. Step 2: Add the hours column. L0 05 7+2+!(carryoverl = 10 hours Thus, Rohan reached office at j.O:05 a.m. Example 2: A primary school starts at 8:40 a.m. and closes at 12:30 p.m. Find the total duration for which the school remains open. To find the total duration, subtract the starting time from the closing time. Starting time = 8;40 a.m. Closing time = L2:30 p.m. Therefore, to find the time duration, subtract g hours 40 minutes from 12 hours 30 minutes. Write minutes in minutes column, hours in hours column and then subtract. Step 1: Subtract the minutes colrrmn. We cannot subtract 40 from 30 as d-d25 30 < 40. So, borrow L hour from hours column and then subtract. 40 Since, t hour = 60 minutes ... 60 + 30 = 90 minutes Thus, 90 - 40 = 50 minutes 3 50

Step 2: Subtract the hours column. Since, L hour is borrowed by the minutes column, so we are left with 12 - 1= 11 hours. Thus, L1-8 = 3 hours. Thus, the school remains open for 3 hours 50 minutes. 3:Example Farzana's school closes at 3:30 p.m. and her school core of o.m. ond remains open for 7 hours. At what time does her p.m. during colculotion school start? To find the starting time, count backward from the closing time and subtract the total duration of time. Ending time = 3:30 p.m. Total time = 7 hours Let us count backward using the timeline. 9 t1, 12 3 p.m. Therefore, starting time = 3:30 p.m. - 7 hours = 8:30 a.m. Calculating the Number of Days Example 1: In class 5 of a school, unit tests started on loth June and lasted for 5 davs. On which dav was the last test held? To find the last day of the test, add the starting date and the total time d uration. Starting date = 10th June Total duration=5days Therefore, last day of the test = j.Oth June + 4 days (1oth June is included) = 14th June Thus, the last test was held on 14th June. Example 2: Humaira started reading a book on 2oth March and finished it on 9th April of the same year. How long did she take to read the book? To find the time duration, subtract the starting date from the finishing date.

rc Starting date = 20th March Finishing date = gth April Number of days from 2oth March to 3l.st March = 12 days Number of daysfrom 1st April to gth April = 9 days Total time = 12 days + 9 days = 21 days Thus, Humaira took 21 days to read the book. Example3: The rehearsal for a show went on for 20 days and the last day of the rehearsal was on 22nd July. When was the rehearsal started? To find the starting date, count backward and subtract the total time duration from the finishing date. Finishing date = 22nd July Total time duration = 20 days Therefore, starting date = 22 - 19 = 3rd July Thus, the rehearsai was started on 3rd July. L. Find the starting time for the followins activities. a. Finishing time = 7 iI2 p.m. b. Finishing time = 11:56 p.m. Time duration = 5 hours 25 minutes Timeduration=4hours d. Finishing time = 9:40 p.m. Time duration = 6 hours 10 minutes c. Finishing time = 12 noon Time duration = 10 hours 4g minutes 2. Find the finishing time for the following activities. a. Starting time = 2:10 a.m. D. Starting time = 3:05 p.m. Time duration = 5 hours 20 minute5 Time duration = 3 hours 20 minutes q. Starting time = 7:35 a.m. Time duration = 7 hours 45 minutes c. Starting time = 5:10 a.m. Time duration = 14 hours 50 minutes 3. Find the time duration for the following activities. a. Starting time = 3:20 a.m. b. Starting time = 4:26 p.m. Finishing time = L0;15 a.m. Finishing time = 11:34 p.m.

c. Starting time = 12 midnight d. Starting time = 8:48 p.m. Finishing time = 4:32 a.m. Finishing time = 11:5S p.m. 4. Find the starting date for the following activities, considering the year has 365 days. a. Finishing date = 15th August b. Finishing date = 2nd March daysTime duration = 11\" c. Finishing date = 14th November Time duration = 22 davs Time duration = 40 days d. Finishing date = 2oth May Time duration = 35 davs 5. Find the time duration for the following actjvities. a. Starting date = 26th July b. Starting date = lsth October Finishing date = 25th September Finishing date = lsth November c. Starting date = Lst February d. Starting date = 2oth June Finishing date = 28th February Finishing date = 17th November 6. Find the finishing date for the following activities. a. Starting date = 1lth September b. Starting date = 27th May Time duration = 25 days Time duration = 44 days c. Starting date = 20th January d. Starting date = 14th April daysTime duration = 12 Time duration = 21 days l7. Khushi and Keerti are twin sisters. Kh ush i joined a schoor when she was 3 years month old. Keerti joined the school after 1 year g months, from the day when Khushi joined. How old was Keerti when she joined the school? 8. A movie started at 6:40 p.m. and finished at 10:LO p.m. What was the duration of the movie? 9. Count the number of days between 15th August and 18th September (include both the oays,l. 10' An express train takes 3 hours 20 minutes to cover a distance between station A and station B. A goods train takes 5 hours 10 minutes to cover the same distance. How much more time is taken by the goods train than the express train? 11 A musicar show started at 6:30 p.m. and frnished at 10:15 p.m. what was the duration of the musical show? 12. Akash is 10 years 8 months old. His father is 30 years 9 months elder to him. How old is his father? #.

l,ydEl nanut, a student of class 5, takes 45 minutes to reach his school. The school gate closes at 8:L0 a.m. What time must he start from his home to reach the school on time? Present in your class the importance of discipline in our lives. In a year, February has only 28 days. Every day of a week in February occurs only 4 times. For any day to occur 5 times, it has to be a leap year. For example, 1st February in 2012 was a Wednesday, so 29th February was the fifth Wednesday and 1st March was a Thursdav. Raman is older than Sheeba by 3 years 6 months. Sheeba is younger than Priya by l year 5 months. lf Priya is 10 years 2 months old, how old is Raman? MlYrvY Pr 'r-o' iect 'iJltt i -.**.^_. -.----n. 1. Note down the starting time and finishing time of different activities performed by you during a day' For example, morning assembly, playing, watching TV' etc. Calculate and record the time duration of each event' Compare it with Your friends. 2. Record the date of birth of each member of your family and between their ages in terms of number of- finO-tt'\" diff\"t\"n.\" oavs. Temperature 536r A mug of coffee is hot whereas an ice cream is cold. ^\\llOr.c But how can we determine whether something is hot or cold? It is determined by the temperature. Temperature is a measurement of how hot or cold a place or an object is.

Thermometer is used to measure temperature. A thermometer has two -= scales-Celsius scale (.C) and Fahrenheit scale (.F). The basic unit of measurement is degree and the standard unit is so- degree Celsius, also called as Centigrade. The Celsius scale is markeo '= *== from 0' to 100\". 0 \"C is the freezing point of water and 1OO.C is the boiling point of water. In the Fahrenheit scale, the freezing point ofwater is 32.F and the boiling point of water is 212 \"F. On comparing the two scales, we get 0.C = 32.F and 100\"C = 212.F, where C and F indicate the scales that are used. 'I I Conversion of Celsius Scale into Fahrenheit Scale tTeomcopnevrearttuaretebmy.pq;earantdurtheefnroamddC3el2situosits.caTlheuisn,to\"rF=a(/h.rcen\"h^!e)\\it+sacazle, multiply the Example: Temperature of a hot glass of milk is 65.C. Convert this temperature into Fahrenheit scale. Temperature in Celsius scale = 65.C |)*Therefore, temperature in Fahrenheit scale = fos \" sz (13 x $1 132 1L7 +32=149\"F Thus, the temperature in Fahrenheit is 149\"F. Conversion of Fahrenheit Scale into Celsius Scale To convert a temperature from Fahrenheit scare into cersius scare, first subtract 32 from the temperature and then muttipty OV l-. rnus, \"C = (\"r - 3Z) x f_ Example: Convert 113.F into Celsius scale. Temperature in Fahrenheit scale = 1j.3\"F x+Therefore, temperature in Celsius scale = (113 - 32) x+=81 J9 =9x5=45'C Thus, the temperature in Celsius is 45.C.

1,. Define the following terms. a. Temperature b. Thermometer What is the freezing point and boiling point of water in Fahrenheit scate? 3. Convert the following temperatures Into Fahrenheit scale. a. 35 'C b. 45 \"C c. 100'c e. 85'C f. 60'c d. 70\"c 2L2\"F 4. Convert the following temperarures Into Celsius scale. a. L22\"F b. 1s8.F d. 1,40 \"F e. 302'F t. Motqg lian A-T!I]UV TodDhafrryaae.wnewgtlerheixteeafomfratmphcleeeesdotimfhbaaeevtcweilnoebc1eek2nes_nhthhoodewuornitnwecgtoofotcihkmrayfenoodrufsmo. raandt diaffntehdreezndt+eag_cri\"toiuviut,ie\"l.\"s[r.upiier.rurf\"oror.mr,,.ehdo\" obaoyngy*loreiutfeodrutmhrieengdt.ytphee Wake-up time Homework time Lunch time 6:00 a.m. 3:40 p.m. 2:00 p.m. 6:00 hours L5:40 hours 14:00 hours Straight angle: j.80\" Obtuse angle: 140. Acute angle: 60.

Complete the following table. Starting time/date' Finishing time/date o. 3:20 p.m. 4 hours L0 minutes 5:30 a.m. c. 12th September 31st October zln dew< d. e. 8:30 a.m. 8th lanr ranr 2 hours 20 minutes f. 21st March 32 days 20th December g. 1st November Convert L48 minutes into hours and minutes. Convert 78 seconds into minutes and seconds. Tick (r') the correct statement and cross out (r) the wrong statement. a. Cricket coaching at 3.00 a.m. b. Breakfast at 8:30 a.m. c. Dinner at 9:00 a.m. d. Snacks break in school at 10.30 p.m. Rhea takes 45 minutes to reach school. lf her school starts at 9 a.m., then at what time should she leave from home? Anjali was born on 18th April. How old will she be on 3oth November of the same vear? A TV programme runs from 7:30 p.m. to 8:22 p.m. lf the commercial advertisement is for 18 minutes, then what is the actual duration of the programme? How much time has elapsed between L1:20 a.m. and 11:10 p.m.? Convert the following temperatures into Fahrenheit scale.. a. !20\"c b. 255\"C c. 320'C d. 445\"C e. 500'c Convert the following temperatures into Celsius scale. e. 932'F a. 248\"F b. 158\"F c. 536\"F d. 635 \"F

A o WonrsxeEFr/l$l' Anju wants to watch a movie in a house at 5:OO p.m. lt takes her 45 way, she is delayed by 50 minutes the movie? ,o*i.i\"1. mall, which will start at 6:00 p.m. She reaves her minutes to reach th\" rnuf f irorn f,\"|. flouse. On her as her car broke down. iui,, ,h\" n\" tor. 2. Kailash was born on 1st April, 2010. How many days old will he 2 February 20L1? be on iiri\"#a*\",3. t3rKhe;eu4an5cjahopleu.rsrmentt.euhyaren?nssdWttafoihtnioaahntirsyisahnrtoehdmaecbehtotimeoasrwednhstiastfhkoheeronmatrbafeeyinsattrtiaav4tian:9l1.:0t2Ho0peta.amlet.ema. vw.heHihsmeahti,rse\"isahctohhueessetohatiatsrghd:o0um0raeatr.imoonw.,nofat 4. d.a. b. c.Convert the given temperatures into Fahrenheit scale. 1.40'C 75'C 95'C 60'c 5. Convert the given temperatures into Celsius scale. a. 77'F b. 95\"F c. \"F1.67 d. 5O.F 6. Piyali was born on 1st December, 2012. She joined school when and 6 months old. On which date did she join the school? she was 2 years f[EfHIEtr|! E E !r!!!!r!!!!!!!!!i! ttEgHt

Moths Around Us Rita goes to the market to buy vegetables. She approaches a vegetable seller. Rita : From where do you get so many vegetables, aunty? Seller : I grow them in my farm. Rita : Why? Seller : To make money. Rita : But how? Seller : lspend { 1O0 to grow vegetables and get { 140 by selling them. Sq my earning is { 40, which is my profit. Rita : Do you always get a profit? :Seller No. Sometimes I am not able to sell all the vegetables that lgrow. Then it is a loss. Rita was curious to know more about the terms,profit, and ,Loss,. She decided to ask this to her maths teacher. Profit and Loss A shopkeeper buys goods from a whoresarer at a certain price. This price is caled the cost price, denoted by CP. He then sells the goods at another price to the customer which is called the selling price, denoted by Sp. lf the selling price is higher than the cost price, the shopkeeper will make a profit, denoted by p. profit is also called as gain. And if the cost

b price is more than the selling price, the shopkeeper will have a loss, denoted by L. lf cost price and selling price are equal, there will be no profit and no loss. Calculating Prof it and Loss When SP > CP, there is a profit. P = SP - CP i.e., Profit = Selling Price - Cost Price When CP > SP, there is a loss. t = CP - SP i.e., Loss = Cost Price - Selling Price lmagine that a fruit seller buys one dozen apples from the market at { 10 per apple and sells each apple for { 12. ICost price of one dozen apples = { L0 x 1.2 = L2O Selling price = 7 1-2 x 12 = 1 1\"44 Since SP > CP, there will be a profit. Profit-SP-CP Thus, profit = 7 1-44 - 7 I20 = 7 24 Suppose, out of the 12 apples, 4 apples are rotten. So, he can sell only 8 a pples. Thus, selling price = { 12 x 8 = {96 tBut cost price was 10 x 12 = t 120 Since CP > SP, there will be a loss. Loss=CP-SP Thus, loss = CP - SP = { 120- { 96 = ( 24 Example 1: A shopkeeper bought one dozen eggs for { 48, but two of them were rotten. So, he sold the remaining eggs for { 5 each. Find his profit or loss. CP of 12 eggs = { 48 Since 2 eggs were rotten, he can sell only 12-2 = 10 eggs. SPofl0eggs=?5x10={50 Since SP > CB there will be a profit. Therefore, profit = SP - CP ={s0-{48={2 Thus, the shopkeeper will have a profit of { 2.

a Example The cost price of a TV set is { 22900. lf it is sold at { 21500, then find the ross. Cost price of the TV set = t 22,900 Selling price of the TV set = { 2j.,500 Therefore, loss = CP - Sp ={22900-T21s00=(1400 Thus, loss on selling the TV set is { 1400. Example 3: The cost price of a bag is { 449 and its selling price is { 345. Find the loss. Cost price of the bag = 7 449 Selling price of the bag = 1 345 Therefore, loss = Cp - Sp ={449-{345=1104 Thus, loss on selling the bag is 1104. Example 4: Rahul bought an old washing machine for { 15000. He spent { 1225 on repairing it and then sold it for I 18549. What is his profit or loss? Price of the washing machine = { 15000 Expenses on its repajr = { 1225 Total cost = { 15000+{ 1225 = { L6225 Selling price ofthe washing machine = { 18549 Since 5P > Ce there will be a profit. ITherefore, profit = Sp _ Cp = { 18549 _ { 16225 = 2324 Thus, there will be a profit of { 2324. Find profit or loss for the followingl a, CP={124,5P={L53 b. CP={345,SP={550 c. CP=?2878,5P={1878 d. CP=?2456,SP=(1675 e. CP={32323,SP=t43454 f. CP={77654,SP={98987 2. rf the cost price of a T-shirt is ( 343 and the shopkeeper se||s it at a price of { 544. then find the profit made by the shopkeeper.

{5. Atul bought a refrigerator for ? 12740 and sold it for 10280. What is his profit or loss? Sameer bought a scooter for { 8450, spent { 2150 on its repair and then sold it for { 10000. What is his profit or loss? l'-ygl eriVa and ner friends made beautiful greeting cards and sold them to a gift ga[ery. They spent ? 900 in purchasing the preparation material for the cards. They sold 100 cards at the rate of { 10 each. Find their profit. The profit earned by Priya and her friends was donated by them to an NGO in their localitv. What value does this act of theirs depict? Calculating Cost Price We know that, P = Sp - Cp and L = Cp _ Sp Thus, if profit and selling price are given, we can find the cost price as Cp = Sp _ p or, Cost Price = Selling price - profit And if loss and selling price are given, we can find the cost price as Cp = Sp + L or, Cost Price = Selling price + Loss Example r.: Anju sold her bicycle for { 3254 and made a profit of { 645. what is the cost price of the bicycle? SP of the bicycle = ? 3254 profit = { 645 Therefore, Cp = Sp _ p = {3254_{G45 = { 2609 Thus, the cost price of the bicycle is { 2609. Example 2: Mr Vishwanathan earns a profit of { 11850 by selling a bike for < 92500. What is the cost price of the bike sold? Profit earned by selling the bike = { 11850 5P ofthe bike = t 92500 Therefore, CP = Sp - p = {92s00-?11850 = { 80650 Thus, the cost price of the bike is { 80650.

Example 3: Tanya sold a pair of goggles for ( 1340. She suffered a loss of { 344. Find the cost price of the goggles. SP ofthe goggles = t 1340 Loss suffered = {344 Therefore, CP = SP + L = { 1340+?344 = { 1684 Thus, the cost price of the pair of goggles is { 1684. 4:Example Ramya sold her dishwasher for ? 13445, at a loss of ? 2450. Find the cost price of the dishwasher. SP ofthe dishwasher = { 13445 Loss suffered = {2450 Therefore, CP = 5P + L = {L3445+t2450 = t 15895 Thus, the cost price of the dishwasher is { j.5895. t fr .e55 1. Find the cost price for the following: a. 5P={ L42, profit ={ 22 b. SP=?342, loss={94 c. SP=?2345, loss={443 d. SP = { 5453, profit = { 545 f. SP= { 76516, loss={ L324 e. SP =? 57453, profit = { 2322 h. SP={43526, loss=t6538 g. SP={87654, profit={ 11554 2. lf the selling price of a video game is { 778 and profit is ? 220, then find the cost price of the video game. 3. Mr John sold a washing machine at a loss of { 1800. tf the selling price of the washing machine is I 11800, what will be the cost price of the washing machine? 4. Subhash sold his digital camera for ( 8820, at a loss of { j.280. What is the cost price of the digital camera? 5. Rehman sold his music system for { 42000, at a profit of { 4800. What is the cost price of the music system? Ft l l83l ad-f

Calculating Selling Price We know that, P = SP - CP and L = CP - 5P Thus, if profit and cost price are given, we can find the selling price as SP = CP + P or, Selling Price = Cost Price + Profit And, if loss and cost prlce are given, we can find the selling price as SP = CP - L or, selling Price = Cost Price - Loss Example 1: A shopkeeper bought a watch for { 678 and made a profit of ? 122 on selling it. Find the selling price of the watch. CP of the watch = ( 678 Profit on selling = { 122 Therefore, sP = cP + P = {678+{122=<800 Thus, the selling price of the watch is { 800. Example 2: Sanjay bought an old car for { 80000 and spent { 11200 on its repair. At what price should he sell the car if he wants to make a profit of { 9000? Price of the car = { 80000 Expenses on its repair = { 1.1200 Total cost = { 80000 + { 11200 = { 91200 Profit to be made = { 9000 Therefore,SP = CP + P = {9L200+t9000 = t 100200 Thus, he should sell the car for { 100200 to make a profit of { 9000. Example 3: A shopkeeper bought 5 flower vases for { 1655. He sold the same at a loss of { L44. What is the selling price of vases? CP ofthe vases = t 1655 Loss incurred = {144 Therefore, sP = cP - L = (L655-{144={1511 Thus, selling price of the vases is { 1511.

Example 4: Mr Moorthy bought a laptop for { 85900. But he incurs a loss of { 8450 by selling it. What is the selling price of the laptop? CP ofthe laPtoP = t 85900 Loss incurred = {8450 Therefore, SP = CP - L = t 85900 - { 84so =7 774s0 Thus, the selling price of the laptop is { 77450. 1-. Find the selling price for the following: a. CP = ? 234, profit = { 65 b. CP={868, loss={74 c. CP={1324, loss=t149 d. CP = { 4587, profit = ? 320 e. CP = { 1L243, profit = { 276 f. CP =7 34287,loss = { 645 g. CP = t 54638, profit = 7 447 h. CP=t87467,loss={1234 2. Cost price of 1 dozen pens is { L50 and profit made on selling them is ? 25. Find their selling price. 5. A shopkeeper bought a playstation for ? 35986. On selling it, he suffered a loss of { 1876. At what price did he sell the playstation? 4. Nisha bought a juicer worth T 5436 and made a profit of { 386 by selling it. At what price did she sell the juicer? 5. Akash bought a study table for { 12986 and suffered a loss of { 1340 by selling it. At what price did he sell it? Unitary Method Unitary method is the method of finding the value of a certain number of units by finding the value of 1 unit. A unit means one obiect. This method comprises two steps. Step1: Findingthevalue ofone unit, i.e., dividethetotal value bvthetotal numberof untts. Step 2; Finding the value of the required number of units, i.e., multiply the value of one unit by the required number of units.

Example L: lf the cost of 5 pens is { 50, then find the cost of 8 pens' Cost of 5 pens = { 50 lHere, 5 is the total units and { 50 is the totalvaluel p lCost of '1 pen = < = 110 lValue of unit is { 1ol Therefore, cost of8 pens = { 1-O x 8={ 80 [Multiplying the value of 1 unit with the required number of unitsl Example 2: 40 people can sit in four cabs. How many people can sit in 19 such cabs? Number of people who can sit in 4 cabs = 40 people fNumber of people who can sit in 1ca5 = peoole = 10 people Therefore, number of people who can sit in L9 cabs = 10 x 1'9 = 190 people 1. lf the cost of 5 kg of apples is { 500, then what will be the cost of 27 kg of apples? 2. A bus can travel 120 km in 3 hours. How much distance can it travel in t hours? 3. lf 6 packets can hold 42 candies, then how many candies are there in 14 such packets? 4. Costof7 pencil boxesis{945 Whatwill be the cost of 11 such pencil boxes? 5. 4 cartons can hold 88 mangoes. How many mangoes can 15 cartons hold? 6. cost of 11 books is ( 1\"265. What will be the cost of 8 such books? 7. 1OO questions are solved by 4 children in one hour. How many questions can 12 children solve in one hour? 1,. Kiran bought oranges at the rate of ( 10 for 3 oranges. She sold each orange for { 5. lf she had bought 3 dozen oranges, then what was her total loss or profit? l2. Sumit bought dozen apples for { 1OO on Monday and sold them for { 12 each. He bought another dozen of apples on Tuesday for the same orice and sold them for { 9 each. What is his total loss or profit, including both the davs?

Target Olympiod Raj can buy 1 pineapple and 3 mangoes or 2 pineapples for the money he has. Vishal can buy 2 pineapples and 2 mangoes for ( 40 from the same shop. How much monev does Raj need to buy 3 pineapples and 2 mangoes? Price of 1 pineapple and 3 mangoes = price of 2 pineapples Therefore, price of3 mangoes = priceof 2 pinea pples _ price of lpineapple = Price of L pineapple According to the question, Price of 2 pineapples and 2 mangoes = Price of 2 x 3 mangoes + Price of 2 mangoes Price of 6 mangoes + Price of 2 mangoes i,1A^fu Price of 8 mangoes = t 40 lGiven] 6 Therefore, price of L manso = t_Thus, price of 1 pineapple = x,_= t.. Hence, price of 3 pineapples + price of 2 mangoes +{2x Thus, Raj needs < D[gt $ Ilasr a_g4u!/ Objective: To understand the concept of profit and loss Materials required: Books, pencils, erasers, pencil boxes, school bags, etc., and paper price tags as cost price and selling price Method: Teacher makes price tags, puts two tags on one item and keeps the items on display in the class. Ask the students to serect the price tags as se|ing price and cost price of that item and find the profit or loss accordingly. Try out this activity by putting tags of seling price and profit or loss and by putting tags of cost price and profit or loss.

My Proiect aI I I t Ask your mother the price of the grocery items she buys. Draw a table as shown below in your scrapbook. Name of the Cost of 1 Cost of 10 items Cost of 15 item (<) items ({} item (<) 55.00 15 x 55.00 = 1 kg of rice 10 x 55.00 = 825.00 550.00 fireB Mrs Khanna buys L0 kg of rice from a grocery shop, each kilogram costing -(154. After cooking ,: kg of rice, she wants to return the remaining rice to the shopkeeper, as she was not happy with the quality of rice. The shopkeeper agrees to take back the rice but refuses to give back the money, instead asks her to buy something else. Which one of the following options will exactly fit the bill of the remaining quantity of rice? a. l-0 boxes of washing soap, each box costing t 3g. b. 9 boxes of walnuts, each box costing { 57. c. A dozen tins of talcum powder, each tin costing { 72. l&-

1. Complete the table. Profit ({) Pen 8.00 10.00 Water bottle 20.00 5.00 Pencils 2.00 2.00 Pencil box 58.00 66.00 Socks 35.00 12.00 5.00 4.00 Biscuits 22.00 14.00 4.50 Chocolates lce cream 16.00 50.00 7.00 4.00 ,Notebook 10.00 Toy i:2. price? rtMrDesai sold a computer at a profit of I 3g90. lf the cost price of the compute : is L8280, then what is its selling : :: :3'j;- 4. umang bought furniture for { 30400 and sord it for { 4g600. what is his gain or loss?i : 5haltnt bought a sandwich maker for { 1200. lf she wants to make a profit of { 120,i th\"n at what price should she sell it? S:., i lf thecostof Sbottresof mangojuiceis{3o8,thenfindthecostof r.l simirar bottres i i of mango juice. : 6. A train can travel 342 km in two hours. How much distance can the train travel in 5 hours? : 7. The cost price of a geyser is { 6543 and its selling price is { 7860. Find the profit i or loss. : 8. Tick (r')the correct answer. a. lf the cost of 12 kg of detergent powder is I 5400, what wifl be the cost of 22ke ot i detergent powder? i. { 9000 ii. ? 9900 iii. { 8900 iv { 9500 iii. { 3183 b. lf CP = { 3427 and loss = { 244, find Sp i. t 141s ii. T 4132

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