Question

walking up and down a staircase which work is done positive, negative or zero

Answer 1

work done is zero in this case.

W = f×s cosθ
in this case cosθ=0.

Answer 2

The ladder (or the stairs) don't do any work at all. The reason for the same is that the ladder (or stairs) applies the force on our feet only when our feet are right in contact with the ladder (or the stairs). Thus, the point of application of force doesn't move at all while the force is being applied. Thus, net work done by the ladder (or the stairs) is zero because there is no displacement of the point of application of the force. As soon as the displacement occurs, the force ceases to be applied instantaneously.