P and Q walk up a moving up escalator at constant speeds. For every 5 steps that P takes Q takes 3 steps. How many steps would each have to climb when the escalator is switched off, given that P takes 50 and Q takes 40 steps to climb up the moving up escalator respectively?
Explanation:
Both the person and the escalator are moving in the same direction. In this case, the relative speed would be Speed of (Man + Stairs).
We don’t know the speed of the escalator, so assume that to be e.
Let speed of P be 5a steps/sec and Q's is 3a steps/sec.
P is walking 50 steps and he does it in 50/5a = 10/a secs., but in this 10/a secs, even the escalator must have moved with speed "e". The length moved by it would be 10e/a.
So, we can say the total length is 50 + 10e/a (steps moved by P and the escalator helps P in reaching the top).
Similarly for Q we can write 40 + 40e/3a
Both are moving on the same escalator, hence total number of steps should be same.
50 + 10e/a = 40 + 40e/3a
So, e/a = 3
So total length is 50 + 10e/a = 80.
Hence, option (a).
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