Question

In a group of 800 people, 500 can speak Hindi, and 320 can speak English.

Find:

(i) How many can speak both Hindi and English?

(ii) How many can speak Hindi only?

Answer 1

Let H denote the set of people speaking Hindi and E denote the set of people speaking English.

n(H)= number of people can speak Hindi.

n(E)= number of people can speak English.

n(H∪E)= Total number of people (Number of people speak Hindi or English)

n(H)=500,n(E)=320 and n(H∪E)=800.

Number of people speak both Hindi and English =n(H∩E)

=n(H)+n(E)−n(H∪E) [∵n(H∪E)=n(H)+n(E)−n(H∩E)]

=500+320−800=20

Number of people speak Hindi only =n(H)−n(H∩E)=500−20=480