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 any game is.

• A. 128
• B. 216
• C. 240
• D. 160

Answer 1

Answer: (D)

160

Answer 2

$n ( C ) = 224 , n ( H ) = 240 , n ( B ) = 336$

$n ( H \cap B ) = 64 , n ( B \cap C ) = 80$

$n ( H \cap C ) = 40$, $n ( C \cap H \cap B ) = 24$

$n \left( C ^ { c } \cap H ^ { c } \cap B ^ { C } \right) = n \left[ ( C \cup H \cup B ) ^ { c } \right]$

$= 800 - [ n ( C ) + n ( H ) + n ( B ) - n ( H \cap C )$

$- n ( H \cap B ) - n ( C \cap B ) + n ( C \cap H \cap B ) ]$

$= 800 - [ 224 + 240 + 336 - 64 - 80 - 40 + 24 ]$

$= 800 - 640 = 160$.