In the system shown in the figure, the acceleration of 1 kg mass is

 

If a is downward acceleration of 4 kg block, the upward acceleration of 1 kg block must be 2a. 

The equation of motion on 4 kg block is $4g-2T=4a \dots \left(i\right)$

The equation of motion on 1kg block is $$\begin{gathered} T-1g=1\times 2a \dots \left(ii\right) \\ or 2T-2g=4a \dots \left(iii\right) \end{gathered}$$

On adding (i) and (iii), we get

$2g=8a or a=\frac{g}{4}$

$\therefore$Acceleration of 1 kg block $=2a=\frac{g}{2}upwards$