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) \(39\le x\le63\)
(d) \(x=39\)
Solution
Let
\[ n(A)=63\%,\qquad n(B)=76\% \]
Using,
\[ n(A\cup B)=n(A)+n(B)-n(A\cap B) \]
\[ 100\ge63+76-x \]
\[ 100\ge139-x \]
\[ x\ge39 \]
Also,
\[ x\le63 \]
since intersection cannot exceed the smaller set.
Therefore,
\[ 39\le x\le63 \]
Answer
\[ \boxed{39\le x\le63} \]
Correct option: (c)