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. $39\le x\le 63$
• D. $x=39$

Answer 1

Answer: (C)

Let $A$ and $B$ be the two sets of news channel such that
$n(A)=63$, $n(B)=76$, $n(A\cup B)=100$
Also, $n(A\cap B)=x$
Using, $n(A\cup B)=n(A)+n(B)-n(A\cap B)$
$\Rightarrow 100=63+76-x$
$\Rightarrow x=139-100=39$
Again $n(A\cap B)\le n(A)$
$\Rightarrow x\le 63$
$\therefore 39\le x\le 63$