A survey shows that in a city that 63% of the citizen like tea where as 76% like coffee. If x% like both tea and coffee, then

Let the population of the city be 100. Let A denote the set of citizens who like tea and B denote the set of citizens who likes coffee

$\therefore n\left(A\right)=63$ and $n\left(B\right)=76$

we know that  $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$ 

               $\begin{array}{rcl}n(A\cup B)& \le & 100\\ 63+76-n(A\cap B)& \le & 100\\ 39& \le & n(A\cap B)\end{array}$  

Also $n(A\cap B)\le n\left(A\right)$ 

it implies that $n(A\cap B)\le 63$

And $n(A\cap B)\le n\left(B\right)$ it implies that $n(A\cap B)\le 76$

from the above both results $n(A\cap B)\le 63$

From the above two equations $39\le n(A\cap B)\le 63\Rightarrow \boxed{39\le x\le 63}$