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

Monjur Alahi

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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Salim Ahmed Kawsar

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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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