Question

In a group of $800$ people, $550$ can speak Hindi and $450$ can speak English. How many can speak both Hindi and English?

• A. $100$
• B. $200$
• C. $300$
• D. $400$

Answer 1

Answer: (B)

Let $H$ denote the set of people speaking Hindi and $E$ denote the set of people speaking English. We are given that $n(H)=550$, $n(E)=450$ and $n(H\cup E)=800$
We know that $n(H\cup E)=n(H)+n(E)-n(H\cap E)$
$\Rightarrow n(H\cap E)=n(H)+n(E)-n(H\cup E)$
$\Rightarrow n(H\cap E)=550+450-800=200$
Hence, $200$ persons can speak both Hindi and English.