Assume the weights are resting on a surface, the pulleys and rope are massless, the pulleys are frictionless, and the system is maintained in quasi-equilibrium as the rope is pulled (steady state & small accelerations). In this case, the tension T in the rope is constant everywhere. Now, take a horizontal section through the ropes. ("Cut" them and replace the missing portions of the rope with the tension.) Each weight is experiencing an upward force of 2T.
When 2T >= 20, or T = 10, weight A begins to rise. Once a hits a stop, T must be increased to just above 20 to get Weight B to rise. Similarly, T just above 30 causes C to rise after B stops.
The "trick" with these pulley problems is to section the problem through the cables and show the tension, T. Then you've just got free body problems, in this case subject to the floor constraint.
Oh, also, while the first weight is being lifted, the floor beneath weight B experiences 40 - 20 = 20 units of force, and the floor under C experiences 60 - 20 = 40 units of force. Once B is lifted, the floor under C experiences 60 - 40 = 20 units of force. (Presuming that the labels are weights, and not masses.)