Table of Contents

Toggle## Class 8, Maths, Chapter 5, Exercise 5.2, Solutions

**Q.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?**

**Ans:**

**(i) **As per the pie chart 10% people like classical music.

This 10% shows 20 people.

So, 10 % of total people = 20

⇒ $\frac{10}{100}\times Total\,\,people\,\,=\,\,20$

⇒ $Total\,\,people\,\,=\frac{20}{10}\times \,100$= 200 people

(ii) Light Music is liked by the maximum number of people.

(iii) Total number of CD’s = 1000Number of CD’s for different music are as

follows:

(a) Semiclassical, 20 % of 1000 = $\frac{20}{100}\times 1000\,\,=\,\,200$ CD ‘s

(b) Classical, 10 % of 1000 = $\frac{10}{100}\times 1000\,\,=\,\,100\,\,CD’s$

(c) Folk, 30 % of 1000 CD’s = $\frac{30}{100}\times 1000\,\,=\,\,300\,\,CD’s$

(d) Light Music, 40% of 1000 CD’s $=\frac{40}{100}\times 1000\,\,=\,\,400\,\,CD’s$

**Q.2. A group of 360 people were asked to vote for their favourite 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.**

**Ans: **(i) Winter Season got the most votes.

(ii) Central Angle can be calculated as follows:

Total number of votes = 90 + 120 +150 = 360

(a) Summer season $=\frac{90}{360}\times 36{{0}^{0}}\,\,=\,\,9{{0}^{0}}$

(b) Rainy season $=\frac{120}{360}\times 36{{0}^{0}}\,\,=\,\,12{{0}^{0}}$

(c) Winter season $=\frac{150}{360}\times 36{{0}^{0}}\,\,=\,\,15{{0}^{0}}$

(iii) The pie chart for the given data is:

**Q.3.Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.**

**Ans: **The central angle for each angle can be calculated as:

**Q.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. **

**Ans:**

Total marks obtained by the student are 540. this represents 360°

Now, central angle for 105 marks $=\frac{105}{Total\,\,marks}\times 36{{0}^{0}}=\frac{105}{540}\times 36{{0}^{0}}={{70}^{0}}$

(i) Hindi, has its central angle as 70°. Hence, students score 105 marks in Hindi.

(ii) Angle made by Mathematics = 90° and Angle made by Hindi = 70°.

So, the difference of marks = Maths marks – Hindi marks

= $\left( \frac{9{{0}^{0}}}{36{{0}^{0}}}\times 540 \right)-\left( \frac{7{{0}^{0}}}{36{{0}^{0}}}\times 540 \right)$ = 135 – 105 = 30 marks

(iii) Total of Angles of Social Science and Math = 65°+90°=155°

Total of Angles of Science and Hindi = 80°+70°=150°

Yes, It is clear that sum of marks obtained in Social Science and Math is more than that in Science and Hindi.

**Q.5. The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.**

**Ans:**

to make pie chart, we need make central angle.