Here is my answer for this question. There are two ways to solve this problem.

First Way of Solution:

Let say x is the total number of steps.

According to my question

(x-9)/42.5 = (x-18) / 20
42.5(x-18) =20(x-9)
42.5x - 765 = 20x - 180
22.5x = 585
x=585/22.5
x=26

Speed of the escalator = (26 - 9 )/42.5 = 0.4

Time to reach the top = Total step/speed = 26/0.4 = 65 seconds.


Second way of Solution:

James using 9 step, took 42.5 sec. to reach top.
James using 18 step, took 20 sec. to reach top.

So 9 additional steps take 22.5 sec.
so each step take 2.5 sec.

So Total step in the escalator = 9 + (42.5 / 2.5) = 26

Time to reach top = 26 * 2.5 = 65 sec.


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suresh