It is given that the average atomic mass of the sample of element $X$ is $16.2\,\mu $

Let the percentage of isotope $_8^{18}X$ be $y \%$. Thus, the percentage of isotope $_8^{16}X$ will be $(100- y ) \%$

Therefore,

$18 \times \frac{y}{100}+16 \times \frac{(100-y)}{100}=16.2$

$\frac{18 y}{100}+\frac{16(100-y)}{100}=16.2$

$\frac{18 y+1600-16 y}{100}=16.2$

$18 y+1600-16 y=1620$

$2 y+1600=1620$

$2 y=1620-1600$

$y=10$

Therefore, the percentage of isotope $_8^{18}X$ is $10 \%$.

And, the percentage of isotope $_8^{16}X$ is $(100-10) \%=90 \%$