Suppose the elements $X$ and $Y$ combine to form two compunds $X{Y}_2$ and $X_3{Y}_2$. when $0.1$ mole of $X{Y}_2$ weighs $10g$ and $0.05mole$ of $X_3{Y}_2$ weighs $9g$, the atomic weights of $X$ and $Y$ are

The correct option is C 40 , 30
For $X{Y}_2$:
$0.1\text{mole}$ of $X{Y}_2=10g$
$\therefore 1\text{mole}$ of $X{Y}_2=100g$
$⟹X+2Y=100\dots \left(i\right)$
For $X_3{Y}_2$:
$0.05\text{mole}$ of $X_3{Y}_2=9g$
$\therefore 1\text{mole}$ of $X_3{Y}_2=180g$
$⟹3X+2Y=180\dots \left(ii\right)$
On solving for $X$ and $Y$, we get;
$X=40$
and $Y=30$

Hence, the correct answer is option (a).