Leon who is always in a hurry walked up an escalator while it was moving at the rate of one step per second and reached the top in 30 steps. the next day he climbed two steps per second also while it was moving and reached the top in 42 steps.If the escalator had been stopped how many steps did the escalator have from the bottom to the top.
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I will assume that it is Leon who on the first day was walking at one step per second (kind of slow, really), and not the elevator.
Let $S$ be the number of steps on the escalator, and let $v$ be the velocity of the accelerator, in steps per second.
On the first day, our hero took $30$ steps, and in the $30$ seconds it took, the escalator lifted him by a further $30v$ steps. It follows that