Question

A survey shows that 63% of the people watch a news channel whereas 76% watch another channel .If x% watch both the channel.Then

A.x=35 B.x=63 C.63x39 D.x=39

Answer 1

Let n(A)=63,n(B)=76
Here,n(A U B)=100 (as all the people watch at least one of the 2 channels)
Then,n(A U B)=n(A)+n(B)-n(A n B)
n(A n B)=n(A)+n(B)-n(A U B)
=63+76-100
=139-100
=39
so,x=39

Answer 2

The correct answer is (D)- x= 39.

This can be deduced in the following way:

Percentage of people watching one channel= 63%

Percentage of people watching another channel= 76%

Adding both we get= 139%

But, as we know the total percentage cannot be greater than 100.

It is 39% greater than the total which means few people have been counted twice( i.e.in both the sections).

Therefore, it can deduced from here that 39% watch both the channels and hence are a part of both the percentages.