Q. 383.8( 9 Votes )

# 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 :

**Given:** 63% of the people watch a News Channel whereas 76% watch another channel

**To find:** x% of the people watch both channel, then value of x

Let p% and q% of people watch a news channel and another channel respectively

n(p)= 63, n(q) = 76, n(p ∩ q) = x, n(p ∪ q) 100

We know,

n(p ∪ q) n(p) + n(q) – n(p ∩ q)

⇒ 100 63 + 76 – x

⇒ x 139 – 100

⇒ x 39

Now,

n(p ∪ q) n(p) and n(p ∪ q) n(q)

⇒ x 63 and x 76

Hence, **39** **x** **63**

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