Let atomic weight of A = x

and atomic weight of B = y

$$\therefore$$ Molar mass of A₂B = 2x + y

and molar mass of AB₃ = x + 3y

Now, weight of 0.15 moles of A₂B = (2x + y) 0.15

and weight of 0.15 moles of AB₃ = (x + 3y) 0.15

Given, weight of 0.15 moles of A₂B and AB₃ are equal.

$$\therefore$$ (2x + y)0.15 = (x + 3y)0.15

$$\Rightarrow$$ x = 2y

$$ \Rightarrow {x \over y} = 2$$

$$\therefore$$ Atomic weight of A is 2 times of atomic weight of B.