#### 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?

#### Solution

Let H be the set of people who speak Hindi, and

E be the set of people who speak English

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

*n*(H ∩ E) = ?

We know that:

*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

Thus, 50 people can speak both Hindi and English.

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Solution In a Group of 400 People, 250 Can Speak Hindi and 200 Can Speak English. How Many People Can Speak Both Hindi and English? Concept: Practical Problems on Union and Intersection of Two Sets.