Question

A survey shows that 70% of the Indian like mango where 82% like apple. If x% of Indian like both mango and apples then

(a) x = 52

(b) 52 ≤ x ≤ 70

(c) x = 70

(d) 70 ≤ x ≤ 82

Answer 1

The correct option (b) 52 ≤ x ≤ 70

Explanation:

n(A) = 70 n(B) = 82 n(A ∩ B) = x 

n(A ∪ B) = n(A) + n(B) – n(A ∩ B) 

⇒ n(A ∩ B) = 152 – n(A ∪ B) But n(A ∪ B) ≤ 100

so n(A ∩ B) ≥ 52 

∴ n(A ∩ B) ≤ 70 

∴ 52 ≤ n(A ∩ B) ≤ 70