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
$= n(B - A) = n(B) - n(B \cap A) = 400 - 150 = 250$