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?
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.