Question

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

Answer 1

Let H is the set of people who speak Hindi,
and E is 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 is n(H ∩ E)

use formula,
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

Hence, 50 people can speak both Hindi and English.

Answer 2

Answer:

n(H∩E) = 50

Step-by-step explanation:

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

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

Total number of people in the group n(H∪E) = 400

Number of people who speak both

Hindi and English = n(H∩E) = ?

We know that ,

n(H∩E)= n(H) +n(E) - n(H∪E)

= 250 + 200 - 400

= 450 - 400

= 50

∴n(H∩E) = 50

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