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 ?
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Answer 1

$\huge\red{ \tt \underline{ Solution : - }}$

• Total number of people = 400
• Hindi speaking people = 250
• English speaking people = 200
• Number of people who speaks both languages = ❓

Let H represents the set of hindi speaking people, and E represents the set of English speaking people.

And ∪ represents total number of peoples.

• n(E) = 200
• n(H) = 250
• n(H ∪ E) = 400
• n(H ∩ E) = ?

By using Formula :

n(H ∩ E) + n(H ∪ E) = n(E) + n(H)

n(H ∩ E) + 400 = 200 + 250

n(H ∩ E) = 450 - 400

n(H ∩ E) = 50

Hence

• there are 50 people who speaks both languages

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