A survey shows that 73% of the persons working in an office like coffee, where as 65% like tea, if x denotes the percentage of them, who like both coffee and tea then x cannot be

Let C and T denotes the set of persons like coffee andtea respectively 

$\mathrm{n}\left(\mathrm{C}\right)=73\% , \mathrm{n}\left(\mathrm{T}\right)=65\% , \mathrm{n}(\mathrm{C}\cap \mathrm{T})=\mathrm{x}.$

$\mathrm{n}(\mathrm{C}\cup \mathrm{T})\le 100$

$\Rightarrow \mathrm{n}\left(\mathrm{C}\right)+\mathrm{n}\left(\mathrm{T}\right)-\mathrm{n}(\mathrm{C}\cup \mathrm{T})\le 100$     

$\Rightarrow 73+65-\mathrm{x}\le 100$

$\Rightarrow \mathrm{x}\ge 38$

Also $$\begin{gathered} 73-\mathrm{x}\ge 0\Rightarrow \mathrm{x}\le 73 \\ and 65-\mathrm{x}\ge 0\Rightarrow \mathrm{x}\le 65 \end{gathered}$$

$\therefore 38\le \mathrm{x}\le 65$

So  x = 36 is not posiible