Question

A survey shows that 63% of the people watch a News channel whereas 76% watch another channel. If x % of the people watch both channel, then
(a) x = 35
(b) x = 63
(c) 39 ≤ x ≤ 63
(d) x = 39

Answer 1

Let A denote the percentage of people watching a news channel
Let B denote the percentage of people watching other channel
i.e
n(A) = 63
n(B) = 76
Let n(A∩B) = x
then n(A⋃B) = n(A) + n(B) – n(A∩B) = 63 + 76 – x
n(A⋃B) = 139 – x
i.e x = 139 – n (A⋃B)
Since n(A⋃B) ≤ 100
i.e. 139 – n(A⋃B) ≥ 139 – 100 = 39
i.e. x ≥ 39.
also, n(A∩B) ≤ n(A) and n(A∩B) ≤ n(B)
⇒ n(A∩B) ≤ 63
⇒ 39 ≤ n(A∩B) = x ≤ 63

Hence, the correct answer is option C.