Topic: Dynamics
Concepts: Atwood machine, Statics

Solution:

The tension from the two strings must balance the weight of the pulley. We have

The tension from the three strings must balance the weight of the box:

Adding these two equations, we obtain

We could have directly obtained this by considering the external forces on the pulley-box system. Note the difference in tensions between $T_A$ and $T_B$ is constant. Thus,

If $T_B$ increases to $30\,\mathrm{N}$, then $T_A=T_B+10\,\mathrm{N}=40\,\mathrm{N}$ so the answer is B.