A survey shows that $69\%$ students like mathematics, whereas $75\mathrm{\%}$ like chemistry. If $x\mathrm{\%}$ students like both the subjects, then the maximum value of $x$ is

Let, total students in survey be $100$

If mathematics is represented by $\mathrm{m}$ & chemistry by $\mathrm{c}$, then 
$\mathrm{n}\left(\mathrm{m}\cap \mathrm{c}\right)=\mathrm{x}$
Given, $\mathrm{n}\left(\mathrm{m}\right)=69, \mathrm{n}\left(\mathrm{c}\right)=75$
Now, $\mathrm{n}\left(\mathrm{m}\cup \mathrm{c}\right)=\mathrm{n}\left(\mathrm{m}\right)+\mathrm{n}\left(\mathrm{c}\right)-\mathrm{n}\left(\mathrm{m}\cap \mathrm{c}\right)$
$=69+75–\mathrm{x}$
$=144–\mathrm{x}$
$\because 75\le \mathrm{n}\left(\mathrm{m}\cup \mathrm{c}\right)\le 100$
$75\le 144-\mathrm{x}\hspace{0.17em}\le 100$
$\therefore$ $44\le \mathrm{x}\le 69$