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.

Number of people who speak Hindi = n(H) = 250

Number of people who speak English = n(E) = 200

Total Number of people = n(H ∪ E) = 400

Number of people who can both speak Hindi and English

= 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.