Suppose the elements $$X$$ and $$Y$$ combine to form two compounds $$X{Y_2}$$  and $${X_3}{Y_2}.$$  When $$0.1\,mole$$   of $$X{Y_2}$$  weighs $$10g$$  and $$0.05\,mole$$   of $${X_3}{Y_2}$$  weights $$9g,$$  the atomic weights of $$X$$ and $$Y$$ are

Solution :
Let atomic masses of $$X$$ and $$Y$$ be $${A_X}$$ and $${A_Y},$$ respectively
$$\eqalign{ & {\text{For}}\,X{Y_2},\,{n_{X{Y_2}}} = 0.1 = \frac{{10}}{{{A_X} + 2{A_Y}}} \cr & {\text{or}}\,\,{A_X} + 2{A_Y} = 100\,\,\,\,\,...{\text{(i)}} \cr & {\text{For}}\,{X_3}{Y_2},\,{n_{{X_3}{Y_2}}} = 0.05 = \frac{9}{{3{A_X} + 2{A_Y}}} \cr & {\text{or}}\,\,3{A_X} + 2{A_Y} = 180\,\,\,\,...{\text{(ii)}} \cr & {\text{On solving Eqs}}{\text{. (i) and (ii), we get,}} \cr & \,\,\,\,\,\,\,\,{A_X} = 40\,g\,mo{l^{ - 1}} \cr & \Rightarrow {A_Y} = 30\,g\,mo{l^{ - 1}} \cr} $$