Question

In a group of $760$ persons, $510$ can speak Hindi and $360$ can speak English. Find how many can speak Hindi only.

• A. $250$
• B. $400$
• C. $1270$
• D. $150$

Answer 1

Answer: (B)

$400$

People who can speak both Hindi and English $=n(H\cap E)$

$n\left(P\right)=n\left(E\right)+n\left(H\right)–n(H\cap E)$

$n(E\cap H)=510+360-760=110$

We can see that, $H$ is disjoint union of $n(H–E)$ and $n(H\cap E).$

(If $A$ and $B$ are disjoint then $n(A\cup B)=n\left(A\right)+n\left(B\right))$

$\therefore H=n(H–E)\cup n(H\cap E).$

$\Rightarrow n\left(H\right)=n(H–E)+n(H\cap E).$

$\Rightarrow 510=n(H–E)+110$

$\Rightarrow n(H–E)=400.$