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 player all the three games. The number of boys who did not play any game is

• A. 128
• B. 216
• C. 240
• D. 160

Answer 1

The correct option is D 160

Total no. of boys n(X)=800

Let n(C)=boys who played cricket

n(H)=boys who played hockey

n(B)=boys who played basket ball

$\therefore n\left(C\right)=224,n\left(H\right)=240,n\left(B\right)=336,n(B\cap H)=64,n(C\cap B)=80,n(C\cap H)=40,n(C\cap H\cap B)=24$

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

$\Rightarrow 224+240+336-64-80-40+24=640$

The number of boys who did not play any game=$n\left(X\right)-n(C\cup H\cup B)$

$\Rightarrow 800-640=160$