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Maths-

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Easy

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

160
240
216
128

The correct answer is: 160

Let $U$ be the set of all students in the school. Let $C comma H$ and $B$ denote the sets of students who played cricket, hockey and basketball respectively. Then,
$n open parentheses U close parentheses equals 800 comma n open parentheses C close parentheses equals 224 comma n open parentheses H close parentheses equals 240 comma n open parentheses B close parentheses equals 336$
$n open parentheses H intersection B close parentheses equals 64 comma n open parentheses B intersection C close parentheses equals 80 comma n open parentheses H intersection C close parentheses equals 40$
$a n d comma blank n open parentheses H intersection B intersection C close parentheses equals 24$
$therefore$ Required number
$equals n left parenthesis C ´ intersection H ´ intersection B ´ right parenthesis$
$equals n left parenthesis C union H union B right parenthesis ´$
$equals n open parentheses U close parentheses minus n left parenthesis C union H union B right parenthesis$
$equals n open parentheses U close parentheses minus open curly brackets table row cell n open parentheses C close parentheses plus n open parentheses H close parentheses plus n open parentheses B close parentheses minus n open parentheses C intersection H close parentheses minus n open parentheses H intersection B close parentheses minus n open parentheses B intersection C close parentheses end cell row cell plus n open parentheses C intersection H intersection B close parentheses end cell end table close curly brackets$
$equals 800 minus left curly bracket 224 plus 240 plus 336 plus 336 minus 64 minus 80 minus 40 plus 24 right curly bracket$
$equals 800 minus 640 equals 160$

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