In a group of 1000 people, there are 750 who can speak Hindi and 400 w

1.	In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. How many can speak Hindi only? How many can speak Bengali? How many can speak both Hindi and Bengali?
Answer» Let Total number of People n(P) = 1000 People who speak Hindi n(H) = 750 People who speak Bengali n(B) = 400 We have P = n(H∪B) ⇒ n(P) = n(H)+n(B)– n (H ∩B) = 1000 = 750+400 – n (H ∩B) ⇒n (H ∩B) = 150. ∴ 150 People can speak both languages. H = (H–B) ∪ (H ∩B) (union is disjoint) ∴ n(H) = n(H–B) +n(H ∩B) 750 = n(H–B)+150 n(H–B) = 600 ∴ 600 people speak Hindi. B = (B–H) ∪ (H ∩B) (union is disjoint) ∴ n(B) = n(B–H) +n(H ∩B) 400 = n(B–H)+150 n(B–H) = 250 ∴ 250 people speak Bengali.

In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. How many can speak Hindi only? How many can speak Bengali? How many can speak both Hindi and Bengali?

Answer»

Let

Total number of People n(P) = 1000

People who speak Hindi n(H) = 750

People who speak Bengali n(B) = 400

We have P = n(H∪B)

⇒ n(P) = n(H)+n(B)– n (H ∩B)

= 1000 = 750+400 – n (H ∩B)

⇒n (H ∩B) = 150.

∴ 150 People can speak both languages.

H = (H–B) ∪ (H ∩B) (union is disjoint)

∴ n(H) = n(H–B) +n(H ∩B)

750 = n(H–B)+150

n(H–B) = 600

∴ 600 people speak Hindi.

B = (B–H) ∪ (H ∩B) (union is disjoint)

∴ n(B) = n(B–H) +n(H ∩B)

400 = n(B–H)+150

n(B–H) = 250

∴ 250 people speak Bengali.