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Question

A survey conducted in a city reveals that 48% children like cricket while 77% children like football. Then the percentage of children who like both cricket and football can be
  1. 23
  2. 31
  3. 51
  4. 65


Solution

The correct option is B 31
Let us assume that the number of children in city be 100.
Let C denotes the set of children who like cricket,
and F denotes the set of children who like football.
n(C)=48 and n(F)=77
n(CF)100
n(C)+n(F)n(CF)100
48+77n(CF)100
n(CF)25     (1)

Also, n(CF)min{n(C),n(F)}
n(CF)48     (2)

From (1) and (2),
25n(CF)48

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