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

 let us assume the atomic weights of ' $X$ ' and ' $Y$ ' to be ' $a$ ' and " $b$.

Mass of 0.1mole of XY₂=10g

$\mathrm{i}.\mathrm{e} \mathrm{a}+2\mathrm{b}=10---\left(1\right)$

Mass of 0.05moles of X₃Y₂=9g

$\mathrm{i}.\mathrm{e} 3\mathrm{a}+2\mathrm{b}=9---\left(2\right)$

From(1) and (2), a=40 and b=30

Hence, option (A) is correct.