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

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Consider H as the set of people who speak Hindi

E as the set of people who speak English

We know that

n(H ∪ E) = 400

n(H) = 250

n(E) = 200

It can be written as

n(H ∪ E) = n(H) + n(E) – n(H ∩ E)

By substituting the values

400 = 250 + 200 – n(H ∩ E)

By further calculation

400 = 450 – n(H ∩ E)

So we get

n(H ∩ E) = 450 – 400

n(H ∩ E) = 50

Therefore,

50 people can speak both Hindi and English.

Answer 2

Answer:

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check above image