Question

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

Answer 1

LetH be the set of people who speak Hindi, and

Ebe the set of people who speak English

∴ n(H∪E) = 400, n(H)= 250, n(E)= 200

n(H∩E) = ?

Weknow 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.