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

Let H be the set of people who speak Hindi, and E be the set of people who speak English.
∴n(H∪E)=400, n(H)=250, n(E)=200
n(H∩E)=?
We know that:
n(H∪E) = n(H) + n(E) - n(H∩E)
∴400 = 250 + 200 - n(H∩E)
→400 = 450 - n(H∩E)
→n(H∩E) = 450 - 400
∴n(H∩E) = 50
Thus, 50 people can speak both Hindi and English.