Normal reaction force without contact and placement of force vectors in free body diagram

I the following question, its nowhere stated that the 20 kg block touches the 100 kg block at any point in the motion. Yet, int all solutions I found - Three forces are considered to be acting on the 100 kg block, tension T from string above the block, force F applied and a reaction force N from 20 kg block where N = 20(acceleration of 100 kg block). How can we say that when they never contact? We can see that the shift of length of string to portion above 100 kg block leads to 20 kg block being able to be at same distance from 100 kg one when it moves forward. So what force is moving the 20 kg block? I am not getting its FBD.