Question

In a group of $45$ students, $22$ can speak Hindi only, $12$ can speak English only. How many can speak both Hindi and English?

Answer 1

Given $n(H\cup E)=45$
Let $n(H\cap E)=x$
$n(H\cup E)=n\left(H\right)+n\left(E\right)+n(H\cap E)$
$45=22+12+x$
$\Rightarrow x=11$