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
A
23
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B
31
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C
51
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D
65
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Solution
The correct option is B31 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(C∪F)≤100 ⇒n(C)+n(F)−n(C∩F)≤100 ⇒48+77−n(C∩F)≤100 ⇒n(C∩F)≥25⋯(1)