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

Let H denote the set of people who speak Hindi and E denote the set of people who speak English. Then H ∪ E is the set of people who speak Hindi or English and H ∩ E is the set of people who speak both.
Then n(H) = 250, n(E) = 200 and n(H ∪ E) = 400
We know that 
n(H ∪ E) = n( H ) + n(E) - n(H ∩ E)
.^..  400 = 250 + 200 - n(H ∩ E)
n(H ∩ E) = 450 - 400
n(H ∩ E) = 50
.^..  The number of people who speak both Hindi and English are 50.