Question

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 1

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.