Question

The pie chart given below shows the interest of students in sports. 20 students like table tennis, which is half the number of students who like cricket, and 90 like basketball. Calculate the total number of students in the class.

• A. 160
• B. 180
• C. 220
• D. 200

Answer 1

The correct option is D 200

Let's assume the total number of students in the class is T.
By the angles given, we can find the number of students who like volleyball and football.

Total angle of the pie chart is 360${}^{\circ }$.

Number of students like volleyball
= $\frac{60}{360}$ $\times \text{T}$ = $\frac{\text{T}}{6}$

Number of students like football
= $\frac{30}{360}$ $\times \text{T}$ = $\frac{\text{T}}{12}$

It is also given that 20 students like table tennis.
Number of students like cricket = 2 $\times$ 20 = 40

Number of students like basketball = 90

So, sum of all the students is T.
$\text{T}=\frac{\text{T}}{6}+\frac{\text{T}}{12}+20+40+90$
$\text{T}=\frac{\text{T}}{4}$ + 150

$\text{T}–\frac{\text{T}}{4}$ = 150

$\frac{\text{3T}}{4}$ = 150

$\text{T}=200$