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

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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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In a group of

400

people,

250

can speak Hindi and

200

can speak English. How many people can speak both Hindi and English?

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

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

∴ n (H \cup E) = 400, n (H) = 250, n (E) = 200

n (H \cap E) = ?

We know that:

n (H \cup E) = n (H) + n (E) - n (H \cap E)

∴ 400 = 250 + 200 - n (H \cap E)

\Rightarrow 400 = 450 - n (H \cap E)

\Rightarrow n (H \cap E) = 450 - 400

∴ n (H \cap E) = 50

Thus, 50 people can speak both Hindi and English.

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Question Text	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 Type	Text solution:1
Upvotes	150