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? How many can speak Bengali only? How many can speak both Hindi and Bengali?

• A. $600$, $200$, $300$
• B. $600$, $250$, $300$
• C. $650$, $150$, $150$
• D. $600$, $250$, $150$

Answer 1

Answer: (D)

Let $A$ and $B$ be the sets of persons who can speak Hindi and Bengali respectively.
$n(A\cup B)=1000$, $n(A)=750$, $n(B)=400$.
Number of persons who can speak both Hindi and Bengali
$=n(A\cap B)=n(A)+n(B)-n(A\cup B)$.
$=750+400-1000=150$
Number of persons who can speak Hindi only
$=n(A-B)=n(A)-n(A\cap B)=750-150=600$
Number of persons who can speak Bengali only
$=n(B-A)=n(B)-n(B\cap A)=400-150=250$