Question

In a group of 400 people, 250 can speak Hindi and 200 speak English. How many people can speak both languages? Here, why do you have to take n(H U E) as 400?

Answer 1

because of there is given in the ques un grp 400 people and there is total speaker of english and hindi is 450 so we take 400 h union e

Answer 2

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

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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