**100 steps.
Let v be the speed of the escalator, in steps per second. Let L be the number of steps that you need to take when the escalator stands still.
Upwards (along with the escalator), you walk 1 step per second. You need 50 steps, so that takes 50 seconds. This gives the following equation:
L steps - 50 seconds × v steps/second = 50 steps.
Downwards (against the direction of the escalator), you walk 5 steps per second. You need 125 steps, so that takes 25 seconds. This gives the following equation:
L steps + 25 seconds × v steps/second = 125 steps.
From the two equations follows: L = 100, v = 1. When the escalator stands still, you need 100 steps.**