Question

Out of $800$ boys in a school, $224$ played cricket, $240$ played hockey and $336$ played basketball. Of the total, $64$ played both basketball and hockey; $80$ played cricket and basketball and $40$ played cricket and hockey; $24$ played all the three games. The number of boys who did not play the game is

• A. $128$
• B. $216$
• C. $240$
• D. $160$

Answer 1

The correct option is D

$160$

Explanation for correct option

Calculating the number of boys who did not play the game:

Given,

The total number of boys $n\left(X\right)$ = $800$

Number of boys who played cricket $n\left(C\right)$ = $224$

Number of boys who played hockey $n\left(H\right)$ = $240$

Number of boys who played basketball $n\left(B\right)$ = $336$

Number of boys who play both basketball and hockey $n(B\cap H)=64$

Number of boys who play both cricket and basketball $n(C\cap B)=80$

Number of boys who play both cricket and hockey $n(C\cap H)=40$

Number of boys who play cricket, hockey and basketball $n(C\cap H\cap B)=24$

Calculating the number of pe

Applying the set formula we get:

$n(C\cup H\cup B)=n\left(C\right)+n\left(H\right)+n\left(B\right)-n(B\cap H)-n(C\cap B)-n(B\cap H)+n(C\cap H\cap B)$

$n(C\cup H\cup B)=224+240+336-64-80-40+24$

$n(C\cup H\cup B)=640$

The number of boys who did not play any game is given by:

$$\begin{gathered} =n\left(X\right)-n(C\cup H\cup B) \\ =800-640 \\ =160 \end{gathered}$$

Hence, the correct answer is Option(D).