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# 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 who speak Hindi, and E be the set of people who speak English.

Then,

n (H) = 250, n (E) = 200 and n (H υ E) = 400

We know that n(H υ E) is,

n (H υ E) = n (H) + n (E) - n (H ∩ E)

n (H ∩ E) = n (H) + n (E) - n (H υ E)

n (H ∩ E) = 250 + 200 - 400

n (H ∩ E) = 450 - 400

n (H ∩ E) = 50

Therefore, 50 people can speak both Hindi and English.

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.6 Question 3

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

**Summary:**

It is given that in a group of 400 people, 250 can speak Hindi and 200 can speak English. We have found that 50 people can speak both Hindi and English.

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