RD Sharma Solutions for Class 8 Chapter 25 Data Handling  III (Pictorial Representation of Data as Pie Charts or Circle Graphs) Free Online
EXERCISE 25.1 PAGE NO: 25.12
1. The number of hours, spent by a school boy on different activities in a working day, is given below:
Activities  Sleep  School  Home  Play  Others  Total 
Number of Hours  8  7  4  2  3  24 
Present the information in the form of a piechart.
Solution:
Here, total number of hours = 24
So,
The central angle = (component value/24) × 360°
The central angle for each activity will be calculated as follows
Activity  Number of Hours  Central Angle 
Sleep  8  8/24 × 360° = 120o 
School  7  7/24 × 360° = 105o 
Home  4  4/24 × 360° = 60o 
Play  2  2/24 × 360° = 30o 
Others  3  3/24 × 360° = 45o 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Here, it is 120o. Construct a sector of central angle 120o whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
2. Employees of a company have been categorized according to their religions as given below:
Religious  Hindu  Muslim  Sikh  Christian  Total 
Number of Workers  420  300  225  105  1080 
Draw a piechart to represent the above information.
Solution:
Here, total number of workers = 1080
So,
The central angle = (component value/1080) × 360°
The central angle for each activity will be calculated as follows
Religious  Number of Workers  Central Angle 
Hindu  420  420/1080 × 360° = 144 
Muslim  300  300/1080 × 360° = 102.9 
Sikh  225  225/1080 × 360° = 77.14 
Christian  105  105/1080 × 360° = 36 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
3. In one day the sales (in rupees) of different items of a baker’s shop are given below:
Items  Ordinary bread  Fruit bread  Cakes and Pastries  Biscuits  Others  Total 
Sales (in Rs)  260  40  100  60  20  780 
Draw a piechart to represent the above information.
Solution:
Here, total sales = 780
So,
The central angle = (component value/780) × 360°
The central angle for each activity will be calculated as follows
Items  Sales (in Rs)  Central Angle 
Ordinary bread  260  260/780 × 360° = 195 
Fruit bread  40  40/780 × 360° = 30 
Cakes and Pastries  100  100/780 × 360° = 75 
Biscuits  60  60/780 × 360° = 45 
Others  20  20/780 × 360° = 15 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
4. The following data shows the expenditure of a person on different items during a month. Represent the data by a piechart.
Items of expenditure  Rent  Education  Food  Clothing  Others 
Amount (in Rs)  2700  1800  2400  1500  2400 
Solution:
Here, total amount = Rs 10800
So,
The central angle = (component value/10800) × 360°
The central angle for each activity will be calculated as follows
Items of expenditure  Amount (in Rs)  Central angle 
Rent  2700  2700/10800 × 360° = 90 
Education  1800  1800/10800 × 360° = 60 
Food  2400  2400/10800 × 360° = 80 
Clothing  1500  1500/10800 × 360° = 50 
Others  2400  2400/10800 × 360° = 80 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
5. The percentages of various categories of workers in a state are given in the following table.
Categories  Cultivators  Agricultural Labourers  Industrial Workers  Commercial Workers  Others 
% of workers  40  25  12.5  10  12.5 
Present the information in the form of a piechart.
Solution:
Here, total % of workers = 100%
So,
The central angle = (component value/100) × 360°
The central angle for each activity will be calculated as follows
Categories  % of workers  Central angle 
Cultivators  40  400/100 × 360° = 144 
Agricultural Labourers  25  25/100 × 360° = 90 
Industrial Workers  12.5  12.5/100 × 360° = 45 
Commercial Workers  10  10/100 × 360° = 36 
Others  12.5  12.5/100 × 360° = 45 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
6. The following table shows the expenditure incurred by a publisher in publishing a book:
Items  Papers  Printing  Binding  Advertising  Miscellaneous 
Expenditure (in %)  35%  20%  10%  5%  30% 
Present the above data in the form of piechart.
Solution:
Here, total Expenditure (in %) = 100%
So,
The central angle = (component value/100) × 360°
The central angle for each activity will be calculated as follows
Items  Expenditure (in %)  Central angle 
Papers  35%  35/100 × 360° = 126 
Printing  20%  20/100 × 360° = 72 
Binding  10%  10/100 × 360° = 36 
Advertising  5%  5/100 × 360° = 18 
Miscellaneous  30%  30/100 × 360° = 108 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
7. Percentage of the different products of a village in a particular district are given below. Draw a pie chart representing this information.
Items  Wheat  Pulses  Jwar  Groundnuts  Vegetables  Total 
%  125/3  125/6  25/2  50/3  25/3  100 
Solution:
Here, total % = 100%
So,
The central angle = (component value/100) × 360°
The central angle for each activity will be calculated as follows
Items  %  Central angle 
Wheat  125/3  (125/3)/100 × 360° = 150 
Pulses  125/6  (125/6)/100 × 360° = 75 
Jwar  25/2  (25/2)/100 × 360° = 45 
Groundnuts  50/3  (50/3)/100 × 360° = 60 
Vegetables  25/3  (25/3)/100 × 360° = 30 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
8. Draw a pie diagram for the following data of expenditure pattern in a family:
Items  Food  Clothing  Rent  Education  Unforeseen events  Medicine 
Expenditure (in %)  40%  20%  10%  10%  15%  5% 
Solution:
Here, total % = 100%
So,
The central angle = (component value/100) × 360°
The central angle for each activity will be calculated as follows
Items  Expenditure (in %)  Central angle 
Food  40%  40/100 × 360° = 144 
Clothing  20%  20/100 × 360° = 72 
Rent  10%  10/100 × 360° = 36 
Education  10%  10/100 × 360° = 36 
Unforeseen events  15%  15/100 × 360° = 54 
Medicines  5%  5/100 × 360° = 18 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
9. Draw a pie diagram of the areas of continents of the world given in the following table:
Continents  Asia  U.S.S.R  Africa  Europe  North America  South America  Australia 
Area (in million sq.km)  26.9  20.5  30.3  4.9  24.3  17.9  8.5 
Solution:
Here, total Area = 133.3 million sq.km
So,
The central angle = (component value/133.3) × 360°
The central angle for each activity will be calculated as follows
Continents  Area (in million sq.km)  Central angle 
Asia  26.9  26.9/133.3 × 360° = 72.6 
U.S.S.R  20.5  20.5/133.3 × 360° = 55.4 
Africa  30.3  30.3/133.3 × 360° = 81.8 
Europe  4.9  4.9/133.3 × 360° = 13.2 
North America  24.3  24.3/133.3 × 360° = 65.6 
South America  17.9  17.9/133.3 × 360° = 48.3 
Australia  8.5  8.5/133.3 × 360° = 23 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
10. The following data gives the amount spent on the construction of a house. Draw a pie diagram.
Items  Cement  Timber  Bricks  Labour  steel  Miscellaneous 
Expenditure (in thousand Rs)  60  30  45  75  45  45 
Solution:
Here, total Expenditure = 300 thousand rupees
So,
The central angle = (component value/300) × 360°
The central angle for each activity will be calculated as follows
Items  Expenditure (in thousand Rs)  Central angle 
Cement  60  60/300 × 360° = 72 
Timber  30  30/300 × 360° = 36 
Bricks  45  45/300 × 360° = 54 
Labour  75  75/300 × 360° = 90 
Steel  45  45/300 × 360° = 54 
Miscellaneous  45  45/300 × 360° = 54 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
11. The following table shows how a student spends his pocket money during the course of a month. Represent it by a pie diagram.
Items  Food  Entertainment  Other Expenditure  Savings 
Expenditure  40%  25%  20%  15% 
Solution:
Here, total Expenditure = 100%
So,
The central angle = (component value/100) × 360°
The central angle for each activity will be calculated as follows
Items  Expenditure  Central angle 
Food  40%  40/100 × 360° = 144 
Entertainment  25%  25/100 × 360° = 90 
Other Expenditure  20%  20/100 × 360° = 72 
Savings  15%  15/100 × 360° = 54 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
12. Represent the following data by a pie diagram:
Items of expenditure  Expenditure 
Family A Family B  
Food  4000 6400 
Clothing  2500 480 
Rent  1500 3200 
Education  400 1000 
Miscellaneous  1600 600 
Total  10000 16000 
Solution:
Here, the total expenditure of family A = 10000 and family B = 11680
The central angle for family A = (component value/10000) × 360°
The central angle for family B = (component value/11680) × 360°
Hence, the central angle for each activity will be calculated as follows
Items of expenditure  Expenditure of Family A  Expenditure of
Family B
 Central angle of Family A  Central angle of
Family B

Food  4000  6400  4000/10000 × 360° = 144  6400/11680 × 360° = 197.3 
Clothing  2500  480  2500/10000 × 360° = 90  480/11680 × 360° = 14.8 
Rent  1500  3200  1500/10000 × 360° = 54  3200/11680 × 360° = 98.6 
Education  400  1000  400/10000 × 360° = 14.4  1000/11680 × 360° = 30.8 
Miscellaneous  1600  600  1600/10000 × 360° = 57.6  600/11680 × 360° = 18.5 
Now, the piechart for Family A and Family B can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
13. Following data gives the break up of the cost of production of a book:
Printing  Paper  Binding charges  Advertisement  Royalty  Miscellaneous 
30%  15%  15%  20%  10%  15% 
Draw a piediagram depicting the above information.
Solution:
Here, total cost of production of book = 105%
So,
The central angle = (component value/105) × 360°
The central angle for each activity will be calculated as follows
Items  Expenditure  Central angle 
Printing  30%  30/105 × 360° = 102.9 
Paper  15%  15/105 × 360° = 51.4 
Binding charges  15%  15/105 × 360° = 51.4 
Advertisement  20%  20/105 × 360° = 68.6 
Royalty  10%  10/105 × 360° = 34.3 
Miscellaneous  15%  15/105 × 360° = 51.4 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
14. Represent the following data with the help of pie diagram:
Items  Wheat  Rice  Tea 
Production (in metric tons)  3260  1840  900 
Solution:
Here, total cost of production = 6000 metric tons
So,
The central angle = (component value/6000) × 360°
The central angle for each activity will be calculated as follows
Items  Production  Central angle 
Wheat  3260  3260/6000 × 360° = 195.6 
Rice  1840  1840/6000 × 360° = 110.4 
Tea  900  900/6000 × 360° = 54 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
15. Draw a piediagram representing the relative frequencies (expressed as percentage) of the eight classes as given below:
12.6, 18.2, 17.5, 20.3, 2.8, 4.2, 9.8, 14.7
12.6, 18.2, 17.5, 20.3, 2.8, 4.2, 9.8, 14.7
Solution:
Here, total amount = 100.1%
So,
The central angle = (component value/100.1) × 360°
The central angle for each activity will be calculated as follows
Class  Amount (in %)  Central angle 
1  12.6  12.6/100.1 × 360° = 45.3 
2  18.2  18.2/100.1 × 360° = 65.5 
3  17.5  17.5/100.1 × 360° = 62.9 
4  20.3  20.3/100.1 × 360° = 73 
5  2.8  2.8/100.1 × 360° = 10.1 
6  4.2  4.2/100.1 × 360° = 15.1 
7  9.8  9.8/100.1 × 360° = 35.2 
8  14.7  14.7/100.1 × 360° = 52.9 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
16. Following is the break up of the expenditure of a family on different items of consumption:
Items  Food  Clothing  Rent  Education  Fuel etc.  Medicine  Miscellaneous 
Expenditure (in Rs)  1600  200  600  150  100  80  270 
Draw a piediagram to represent the above data.
Solution:
Here, total expenditure = 3000 Rs
So,
The central angle = (component value/3000) × 360°
The central angle for each activity will be calculated as follows
Items  Expenditure (in Rs)  Central angle 
Food  1600  1600/3000 × 360° = 192 
Clothing  200  200/3000 × 360° = 24 
Rent  600  600/3000 × 360° = 72 
Education  150  150/3000 × 360° = 18 
Fuel  100  100/3000 × 360° = 12 
Medicine  80  80/3000 × 360° = 9.6 
Miscellaneous  270  270/3000 × 360° = 32.4 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
17. Draw a pie diagram for the following data of the investment pattern in a five years plan:
Agriculture  Irrigation and Power  Small Industries  Transport  Social service  Miscellaneous 
14%  16%  29%  17%  16%  8% 
Solution:
Here, total investment = 100%
So,
The central angle = (component value/100) × 360°
The central angle for each activity will be calculated as follows
Data  Investment  Central angle 
Agriculture  14%  14/100 × 360° = 50.4 
Irrigation and Power  16%  16/100 × 360° = 57.6 
Small Industries  29%  29/100 × 360° = 104.4 
Transport  17%  17/100 × 360° = 61.2 
Social service  16%  16/100 × 360° = 57.6 
Miscellaneous  8%  8/100 × 360° = 28.8 
Now, the piechart can be constructed by using the given data.
Steps to construct:
Step 1: Draw the circle of an appropriate radius.
Step 2: Draw a vertical radius anywhere inside the circle.
Step 3: Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.
Step 4: Construct other sectors representing other values in clockwise direction in descending order of magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
EXERCISE 25.2 PAGE NO: 25.21
1. The pie chart given in Fig. 25.17 represents the expenditure on different items in constructing a flat in Delhi. If the expenditure incurred on cement is Rs. 112500, find the following:
(i) Total cost of the flat.
(ii) Expenditure incurred on labour.
(ii) Expenditure incurred on labour.
Solution:
(i) By using the formula,
Expenditure incurred on cement = (central angle × Total cost) / 360°
Total cost of the flat = (360° × 112500) / 75o = Rs 540000
(ii) By using the formula,
Expenditure incurred on labour = (central angle × Total cost) / 360°
= (100° × 540000) / 360o = Rs 150000
2. The piechart given in Fig. 25.18 shows the annual agricultural production of an Indian state. If the total production of all the commodities is 81000 tonnes, find the production (in tonnes) of
(i) Wheat (ii) Sugar (iii) Rice (iv) Maize (v) Gram
Solution:
We know that,
Total Production = 81000 Tonnes.
So,
(i) Production of wheat = (central angle of wheat × Total production) / 360°
= (120o × 81000) / 360o = 27000 tonnes
(ii) Production of sugar = (central angle of sugar × Total production) / 360°
= (100o × 81000) / 360o = 22500 tonnes
(iii) Production of rice = (central angle of rice × Total production) / 360°
= (60o × 81000) / 360o = 13500 tonnes
(iv) Production of maize = (central angle of maize × Total production) / 360°
= (30o × 81000) / 360o = 6750 tonnes
(v) Production of gram = (central angle of gram × Total production) / 360°
= (50o × 81000) / 360o = 11250 tonnes
3. The following pie chart shows the number of students admitted in different faculties of a college. If 1000 students are admitted in Science answer the following :
(i) What is the total number of students?
(ii) What is the ratio of students in science and arts?
(ii) What is the ratio of students in science and arts?
Solution:
(i)
Students in science = (central angle × Total students) / 360°
1000 = (100o × Total students) / 360o
Total students = (1000 × 360o)/100o
= 3600 students
∴ Total number of students are 3600.
(ii) Students in arts = (central angle of arts × Total students) / 360°
= (120o × 3600) / 360o = 1200 students
∴ Ratio of students in science and arts is 1000:1200 = 5:6
4. In Fig. 25.20, the piechart shows the marks obtained by a student in an examination. If the student secures 440 marks in all, calculate his marks in each of the given subjects.
Solution:
Marks secured in mathematics = (central angle of maths × Total score secured) / 360°
= (108 × 440) / 360o = 132 marks
Marks secured in science = (central angle of science × Total score secured) / 360°
= (81 × 440) / 360o = 99 marks
Marks secured in English = (central angle of English × Total score secured) / 360°
= (72 × 440) / 360o = 88 marks
Marks secured in Hindi = (central angle of Hindi × Total score secured) / 360°
= (54 × 440) / 360o = 66 marks
Marks secured in social science = (central angle of social science × Total score secured) / 360°
= (45 × 440) / 360o = 55 marks
Subject  Mathematics  Science  English  Hindi  Social Science 
Marks secured  132  99  88  66  55 
5. In Fig. 25.21, the pie chart shows the marks obtained by a student in various subjects. If the student scored 135 marks in mathematics, find the total marks in all the subjects. Also, find his score in individual subjects.
Solution:
Let us calculate the total marks.
So,
Marks scored in mathematics = (central angle of maths × Total marks) / 360°
135 = (90 × Total marks) / 360o
Total marks = (135 × 360)/90
= 540 marks
Now,
Marks scored in Hindi = (central angle of Hindi × Total marks) / 360°
= (60 × 540) / 360o
= 90 marks
Marks scored in Science = (central angle of Science × Total marks) / 360°
= (76 × 540) / 360o
= 114 marks
Marks scored in Social science = (central angle of Social science × Total marks) / 360°
= (72 × 540) / 360o
= 108 marks
Marks scored in English = (central angle of English × Total marks) / 360°
= (62 × 540) / 360o
= 93 marks
Subject  Mathematics  Science  Social science  English  Hindi 
Marks secured  135  114  108  93  90 
6. The following pie chart shows the monthly expenditure of Shikha on various items. If she spends Rs 16000 per month, answer the following questions:
(i) How much does she spend on rent?
(ii) How much does she spend on education?
(iii) What is the ratio of expenses on food and rent?
Solution:
(i) Money spent on rent = (central angle of rent × Total money spent) / 360°
= (81 × 16000) / 360o
= Rs 3600
(ii) Money spent on education = (central angle of education × Total money spent) / 360°
= (36 × 16000) / 360o
= Rs 1600
(iii) Money spent on food = (central angle of food × Total money spent) / 360°
= (135 × 16000) / 360o
= Rs 6000
Ratio of expenses on food and rent is Rs 6000/Rs3600 = 5/3
Ratio = 5:3
7. The pie chart (as shown in the figure 25.23) represents the amount spent on different sports by a sports club in a year. If the total money spent by the club on sports is Rs 108000, find the amount spent on each sport.
Solution:
Money spent on cricket = (central angle of cricket × Total money spent) / 360°
= (150 × 108000) / 360o
= Rs 45000
Money spent on football = (central angle of football × Total money spent) / 360°
= (60 × 108000) / 360o
= Rs 18000
Money spent on tennis = (central angle of tennis × Total money spent) / 360°
= (50 × 108000) / 360o
= Rs 15000
Money spent on hockey = (central angle of cricket × Total money spent) / 360°
= (100 × 108000) / 360o
= Rs 30000