Question

In a group 400 people,250 speak Hindi and 200 speak English. Find (i) How many can speak Hindi and

English. (ii) How many can speak Hindi only. (iii) How many can speak English only

step by step ​

Answer 1

Given:

• Total number of people = 400
• Number of people who speak Hindi = 250
• Number of people who speak English = 200

To find:

• Number of people who can speak Hindi and English both.

Solution:

❐ Let the set of people who speak Hindi be A and the set of people who speak English be B. Therefore,

• n(A ∪ B) = 400
• n(A) = 250
• n(B) = 200
• n(A ∩ B) = ?

No. of people who can speak Hindi and English both,

⇒ n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

⇒ 400 = 250 + 200 - n(A ∩ B)

⇒ 400 = 450 - n(A ∩ B)

⇒ n(A ∩ B) = 450 - 400

⇒ n(A ∩ B) = 50

Hence, no. of people who can speak Hindi and English is 50.

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Answer 2

$Answer:$

Consider H as the set of people who speak Hindi

E as the set of people who speak English

We know that

n(H ∪ E) = 400

n(H) = 250

n(E) = 200

It can be written as

n(H ∪ E) = n(H) + n(E) – n(H ∩ E)

By substituting the values

400 = 250 + 200 – n(H ∩ E)

By further calculation

400 = 450 – n(H ∩ E)

So we get

n(H ∩ E) = 450 – 400

n(H ∩ E) = 50

Therefore, 50 people can speak both Hindi and English.