Question

In a group of $1000$ people there are $750$ who can speak Hindi and $400$ who can speak Bengali. How many can speak Hindi only ?

Answer 1

$n\left(H\cup B\right)=1000$

$n\left(H\right)=750$

$n\left(B\right)=400$

Now, $n\left(H\cap B\right)=n\left(H\right)+n\left(B\right)-n\left(H\cup B\right)$

$\Rightarrow n(H\cap B)=750+400-1000$

$\Rightarrow n\left(H\cap B\right)=150$

Number of people speaking only Hindi $=n\left(H\right)-n\left(H\cap B\right)$

$=750-150$

$=600$