Question

In a group of 800 people, 550 can speak Hindi and 450 can speak English. How many can speak both Hindi and English ?

• A. $100$
• B. $150$
• C. $200$
• D. None of these

Answer 1

The correct option is C $200$

Let H denote the set of people speaking Hindi and E denote the set of people speaking English. We are given :

$n\left(H\right)=550,n\left(E\right)=450,n(H\cup E)=800$

Now,

$n(H\cup E)=n\left(H\right)+n\left(E\right)-n(H\cap E)$

$n(H\cap E)=550+450-800=200$

Hence, 200 persons can speak both Hindi and English.