A survey shows that $73\%$ of Indians like apples, whereas $65\%$ like oranges. What percentage of Indians like both apples and oranges?

Let $A$ be the set of Indians who like apples and $O$ be the set of Indians who like oranges.
Given:
$n(A)=73\%$
$n(O)=65\%$

Let the total percentage of the population be $100\%$, so $n(A\cup O)\le 100\%$.
Using the set formula:

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

Assuming everyone likes at least one of the fruits for finding the intersection value within a standard standard context, $n(A\cup O)=100\%$:

$$100=73+65-n(A\cap O)$$

$$100=138-n(A\cap O)$$

$$n(A\cap O)=138-100=38\%$$

Thus, $38\%$ of Indians like both apples and oranges.