14 November 2016

Question: There is an escalator and 2 persons are climbing down on it.

A climbs down 50 steps and B climbs down 75 steps

while the escalator is moving down.

Given that the time taken by A to take 1 step is equal

to the time taken by B to take 3 steps,

find the total number of steps in the escalator while it is stationary.

Solution:

Let A take 1 step/min. Hence, B takes 3 steps/min.

Let the escalator take n steps/min. Given that A takes 50 steps and hence in the same time, the escalator will take 50n steps. Because A is moving 50 steps,

it means that the time taken is 50 minutes. Therefore, the total no. of steps must be 50 + 50n.

It is given that B takes 75 steps (which means that he takes 25 min). So, in the same time,

the escalator will cover 25n steps. Therefore, the no. of steps must be 75 + 25n.

Equating 50 + 50n = 75 + 25n, we get n = 1. Therefore, the total number of steps = 100.

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