Suppose elements $X$ and $Y$ combine to form two compounds $X{Y}_2$ and $X_3{Y}_2$ when $0.1$ mole of former weight $10g$ while $0.05$ mole of the latter weighs $9g$. What are the atomic weights of $X$ and $Y?$

The correct option is A $40,30$
$X+2Y\to X{Y}_2$ .....(i)

$0.1$ mol of $X{Y}_2=10g$
$\therefore$ 1 mol of $X{Y}_2=100g$

$3X+2Y\to X_3{Y}_2$ ....(ii)

$0.05$ mol of $X_3{Y}_2=9g$

$\therefore$ 1 mol of $X_3{Y}_2=\frac{9}{0.05}=180g$

So, $X+2Y=100$ $(Mol.wtofX{Y}_2=100)$

$3X+2Y=180$ $(Mol.wtof{X}_2{Y}_3=180)$

Solving for X and Y, we get

$X=40g;$ $Y=30g$
Option A is correct.