Let us consider the dumbwaiter separately.
The man standing on it has a mass 80 kg, but the force exerted by him on the elevator is 200N.
He is applying some force on the rope, say F.
80gF=200
You can solve this to know F.
Now the weight of the elevator is 40 kg ang the force exerted by the man is 200N. Let the acc. of the elevator be a.
F20040g=40a.
Substituting F=80g200
we get 80g20020040g=40a
Therefore,40g400=40a
Therefore,a=g10,
Therefore,a=0.2m/s^2
That is 0.2 m/s^2 downwards
