In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali.

Solution:

Let A & B denote the sets of the persons who can speak Hindi & Bengali, respectively.

Given:

$n(A \cup B)=1000$

$n(A)=750$

 

$n(B)=400$

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

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

 

$\Rightarrow n(A \cap B)=150$

Number of persons who can speak both Hindi and Bengali $=n(A \cap B)=150$

Number of persons who can speak only Hindi $=n(A-B)=n(A)-n(A \cap B)$

$=750-150$

= 600

Number of persons who can speak only Bengali $=n(B-A)=n(B)-n(A \cap B)$

$=400-150$

 

$=250$