# Exercise 5.2

Question 1

A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining pie chart shows the findings of this survey.

From this pie chart answer the following −

(i) If 20 people liked classical music, how many young people were surveyed?

(ii) Which type of music is liked by the maximum number of people?

(iii) If a cassette company were to make 1000 CD’s, how many of each type would they make?

Sol :

(i) Number of people who like classical music = 10%

This 10% represents 20 people.

100 % represents = people

Therefore, 200 young people were surveyed.

(ii) From the pie chart, it can be easily observed that the light music is represented by the maximum part of the pie chart (i.e., 40 %). Hence, most of the people like light music.

(iii) Number of CD’s of classical music = 10% of 1000

Number of CD’s of semi-classical music = 20% of 1000

Number of CD’s of folk music = 30% of 1000

Number of cassettes of light music = 40% of 1000

Question 2

A group of 360 people were asked to vote for their favorite season from the three seasons rainy, winter and summer.

(i) Which season got the most votes?

(ii) Find the central angle of each sector.

(iii) Draw a pie chart to show this information.

 Season Number of votes Summer 90 Rainy 120 Winter 150

Sol :

(i) Winter

(ii) Total number of votes = 90 + 120 + 150 = 360

 Season Number of votes In fraction Central angle Summer 90 Rainy 120 Winter 150

(iii) A pie chart can be drawn for the above data as follows.

Question 3

The central angle for each colour can be calculated as follows.

 Colours Number of people In fraction Central angle Blue 18 Green 9 Red 6 Yellow 3

The pie chart of the above data is as follows.

Question 4

The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions.

(i) In which subject did the student score 105 marks?

(Hint: For 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle?)

(ii) How many more marks were obtained by the student in Mathematics than in Hindi?

(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.

(Hint: Just study the central angles).

Sol :

(i) Total marks obtained by the student are 540. Hence, 540 marks represent 360º. The central angle for 105 marks has to be calculated.

Central angle for 105 marks =

Hindi is the subject having its central angle as 70º.

Therefore, the student scored 105 marks in Hindi.

(ii) Difference between the central angles of Mathematics and Hindi

= 90º − 70º = 20º

Marks for 20º central angle =

There is a difference of 30 marks between the score obtained in Mathematics and Hindi.

Therefore, 30 more marks were obtained by the student in Mathematics than in Hindi.

(iii) Sum of central angles of Social Science and Mathematics

= 90° + 65° = 155°

Sum of central angles of Science and Hindi = 80° + 70° = 150°

The sum of the central angles for Social Science and Mathematics is more than that of Science and Hindi. Therefore, the student scored more in Social Science and Mathematics than in Science and Hindi.

Question 5

The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.

 Language Hindi English Marathi Tamil Bengali Total Number of students 40 12 9 7 4 72

Sol :

The central angle for each subject can be calculated as follows.

 Language Number of students In fraction Central angle Hindi 40 × 360º = 200º English 12 × 360º = 60º Marathi 9 × 360º = 45º Tamil 7 × 360º = 35º Bengali 4 × 360º = 20º

A pie chart of the above data is as follows.

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