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Question

A survey show that 63% of the american likes cheese whereas 76% of the american like apples if x% of the american like both cheese and apples find the value of x.

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Solution

Let A denotes, the set of Americans who like cheese and B denotes those who like apples.
Let the population of America be 100 then,
n(A)=63 and n(B)=76
Now n(AB)=n(A)+n(B)n(AB)
N(AB)=63+76n(AB)
N(AB)=139n(AB)
But n(AB)100
So, 139n(AB)100
n(AB)39.......(i)
Now n(AB)n(A) and n(AB)n(B)
So, 39n(AB)63
(63 is smallest between n(A) and n(B))

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