Escalator

April 15, 2009 at 8:26 am 1 comment

There is an escalator. Ram and Sham move down it. Ram takes 50 steps and Sham takes 75 steps while the escalator is moving down. Given that the time taken by Ram to take 1 step is equal to time taken by Sham to take 3 steps. Find the number of steps in the escalator while it is stationary?

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  • 1. narinderberi  |  April 15, 2009 at 9:01 am

    I tend to think of Escalator problems this way:

    1. These are speed-distance-time problems.
    2. Distance = Steps, Time = Time, Speed = Number of Steps per Time
    3. Going up or down the escalator means it is a case for relative speed.

    Let Ram’s speed be a steps per second.
    Thus Sham’s speed is 3a steps per second.

    Time taken by Ram = 50/a – I
    Time taken by Sham = 75/3a – II

    Let total number of steps in the escalator be n.
    And let escalator’s speed be e steps per second.

    Relative speed of Ram = (e + a)
    Relative speed of Sham = (e + 3a)

    Again time taken by Ram = n/(e + a) – III
    And time taken by Sham = n/(e + 3a) – IV

    Equating I and III, and II and IV, we get

    a = e. Thus total number of steps in the escalator are 100.

    Another way to think this can be found at http://puzzles4you.blogspot.com/2009/04/escalator-puzzles.html

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