Forces acting on different parts of the system is shown below.

For block $A$,

$mg-2T=ma$   ...$\left(i\right)$. 

For block $B$,

$T-mg=mb$   ...$\left(ii\right)$. 

And by constraint motion, if $A$ will move by $x$ distance, then $B$ will move by $2x$ distance.

$\left(a\mathit{-}b\right)+a\mathit{=}0$   ...$\left(iii\right)$. 

Solving $\left(\mathrm{i}\right), \left(\mathrm{ii}\right) \mathrm{and} \left(\mathrm{iii}\right)$, we get,

$a=-\frac{g}{5}$ and

$b=-\frac{2g}{5}$.