A survey shows that $73\%$ of the 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.
We are given:

$$n(A)=73\%$$

$$n(O)=65\%$$

Assuming everyone surveyed likes at least one of the two fruits, the total union $n(A\cup O)\le 100\%$.
Using the set union formula:

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

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

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

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

Therefore, $38\%$ of Indians like both fruits.