A and B are two elements which form ${\mathrm{AB}}_2$ & ${\mathrm{A}}_2{\mathrm{B}}_3$ if 0.18 mole of ${\mathrm{AB}}_2$ weighs 10.6g and 0.18  mole of ${\mathrm{A}}_2{\mathrm{B}}_3$ weighs 17.8g. Then :

0.18 mole ${\mathrm{AB}}_2=10.6 \mathrm{grams}$

1 mole ${\mathrm{AB}}_2=\frac{10.6}{0.18}=58.9\Rightarrow \mathrm{A}+2\mathrm{B}=58.9\Rightarrow \left(1\right)$

0.18 mole ${\mathrm{A}}_2{\mathrm{B}}_2=17.8 \mathrm{grams}$

1mole ${\mathrm{A}}_2{\mathrm{B}}_3=\frac{17.8}{0.18}=17.8=98.9\Rightarrow 2\mathrm{A}+3\mathrm{B}=98.9\to \left(2\right)$

Eq :(1) × (2) = 2A + 4B = 117.8

Eq:(2) = 2A + 3B = 98.9

B = 18.9

Substitute B in eq 1

A + 2(18.9) = 58.9

A = 58.9 − 37.8 

A = 21.1