A survey shows that 76% of the Indians like oranges,
Question:

A survey shows that 76% of the Indians like oranges, whereas 62% like bananas. What percentage of the Indians like both oranges and bananas?

Solution:

Let A & B denote the sets of the Indians who like oranges & bananas, respectively.

Given :

$n(A)=76 \%$

 

$n(B)=62 \%$

$n(A \cup B)=100 \%$

$n(A \cap B)=?$

We know :

$n(A \cup B)=n(A)+n(B)-n(A \cap B)$

$\Rightarrow 100=76+62-n(A \cap B)$

 

$\Rightarrow n(A \cap B)=38$

Therefore, $38 \%$ of the Indians like both oranges \& bananas.

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