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 least value of x is

Let A be the set of percentage of those people who watch a news channel and B be the set of percentage of those people
who watch another channel.

$\begin{array}{l}n\left(A\right)=63,n\left(B\right)=76,\text{ and }n(A\cap B)=x\\ \because n(A\cup B)\le 100\\ \Rightarrow n\left(A\right)+n\left(B\right)-n(A\cap B)\le 100\\ \Rightarrow 63+76-x\le 100\\ \Rightarrow x\ge 39\\ \text{ Also, }n(A\cap B)\le min.\left\{n\right(A),n(B\left)\right\}\\ \Rightarrow x\le 63\\ \therefore 39\le x\le 63\end{array}$