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

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.

Answer 2

$\large\rm\pink{AnsWeR:}$

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.