This one turned out to be a little difficult for children who do not know algebra, and hence I did not get correct answer from any of the younger kids. Congratulations to Ruchir Godura and Varun Gupta for being the first ones to send the right answer.
I have attempted to explain the answer without algebra for younger children, though I must confess that it is not easy.
For folks who know algebra, I am reproducing the answer sent by Varun:
Assume the staircase to be x. While coming down- Man took 50 steps, in the same time lift came down x-50 steps.
While going up man took 125 steps, lift came down by 125- x steps.
As man ran 5 times as fast as coming down, he would have climbed down 25 steps in same time or ( x-50)/2 lift steps.
Equating (x-50)/2= 125- x, we get steps to be 100.
Hope you enjoyed the puzzle!