Figure shows a system of four pulleys with two masses $m_A=3kg$ and $m_B=4kg$. At an instant, force acting on block $A$, if block $B$ is going up at an acceleration of $3 m/s^2$ and pulley $Q$ is going down at an acceleration of $1 m/s^2$ is 

Writing constraint for the string

$2x_A+2x_B-x_Q+k=\mathcal{l}$

Differentiating twice w.r.t. time $2a_A+2a_B-a_Q=0$

Taking downward direction to be positive

$2a_A+2 (-3)-1=0 ; 2a_A=7; a_A=3.5 m/s^2.$

Positive sign indicates that block is accelerating at $3.5 m/s^2$ in downward direction.

So, force acting $F=3\times 3.5=10.5N$ (downward)