In a group of 500 people, 350 people can speak English, and 400 people can speak French. Find how many people can speak both languages.

A.

750

B.

850

C.

250

D.

150

Correct answer is C

Let F be the set of people who can speak French and E be the set of people who can speak English. Then,

n(F) = 400

n(E) = 350

n(F ∪ E) = 500

We have to find n(F ∩ E).

Now, n(F ∪ E) = n(F) + n(E) – n(F ∩ E)

⇒ 500 = 400 + 350 – n(F ∩ E)

⇒ n(F ∩ E) = 750 – 500 = 250.

∴ 250 people can speak both languages.