In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

Answer
Let H and E is the set of people speaking Hindi and English respectively.
It is given that
People speaking Hindi or English, n(H ∪ E) = 400,
Hindi Speaker, n(H) = 250,
English speaker n(E) = 200.
People can speak both Hindi and English, n(H ∩ E) = ?
Use formula
n ( H ∪ E ) = n ( H ) + n ( E ) – n ( H ∩ E )
Plug the values we get
400 = 250 + 200 - n ( H∩ E )
n ( H ∩ E) = 450 – 400 = 50
Answer
People can speak both Hindi and English, n(H ∩ E) = 50.