Question

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

Answer 1

Let n (P) denote the total percentage of Indians n (O) denotes the percentage of Indians who like oranges, and n(B) denotes the percentage of Indians who ike bananas.

Then, n(P) = 100, n(O) = 76 and n(B) = 62

To find: $n(O\cap B)$

Now,

$n\left(P\right)=n\left(O\right)+n\left(B\right)-n(O\cap B)$

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

$\Rightarrow 100=138-n(O\cap B)$

$\Rightarrow n(O\cap B)=138-100$

= 38

$\therefore 38\%$ of Indians like bpth oranges and bananas.