A survey shows that 73 % of the persons working in an office like coffee, whereas 65 % like tea. If x…

$n\left(C\right)=73, n\left(T\right)=65, n\left(C\cap T\right)=x$, 

Considering that value of $n\left(C\cup T\right)$ cannot exceed $100$ in terms of percentage, we get

$n\left(C\cup T\right)\le 100$

$\Rightarrow n\left(C\right)+n\left(T\right)-n\left(C\cap T\right)\le 100$

$\Rightarrow x\ge 38$

Therefore, $x\ne 36$.

$n\left(C\cap T\right)\le \min \left(n\left(C\right),n\left(T\right)\right) \Rightarrow x\le 65$

$\Rightarrow 38\le x\le 65$

Hence $x$ may assume values $63,54,38$.