A escalator is moving downwards with a uniform speed u. A man of mass m is running upwards on it at a uniform speed v. If the height of escalator is h, the work done by man in going up the escalator is(a) zero(b) mgh(c) mghu/(v-u)(d) mghv/(v-u)

Work done varies with u and v, and is non-zero for u=0

using these clues, answer is (d) 

The answer is mgh.

The escalator donot tends to apply any retarding force of the man (If the escalator has friction the case would be different. Then the escalator would tend to apply frictional force as long as the relative velocity of the man with respect toe the escalator is 0)

As such the man has to only maintain a unform velocity V with respect to the escalator and for this purpose he has to store his energy as potential energy and consequently the only work he needs to do is against gravity and that is equal to mgh.