In a group of 400 people, 250 can speak Hindi and 200 can speak Englis

1.	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» 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.

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»

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

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