In a group of 400 people, 250 can speak ...

NCERT Class XI Mathematics - Sets - Solutions

Question : 52 of 73

Marks: +1, -0

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

Solution:

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

∴ n(H) = 250, n(E) = 200 and n(H ∪ E) = 400,

We know that

n(H ∪ E) = n(H) + n(E) – n(H ∩ E) ⇒ 400 = 250 + 200 – n(H ∩ E)

∴ n(H ∩ E) = 450 – 400 = 50.

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