Shyam and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyam takes three steps for every two steps of Vyom. Shyam gets to the top of the escalator after taking 25 steps, while Vyom takes only 20 steps to reach the top. If the escalator was turned off, then how many steps would they have to take to walk up to the top?
Explanation:
Suppose, Shyam takes 1 min for every 3 steps, then he takes 1/3 min for every step.
For 25 steps, he takes 25/3 min, i.e. 8.33 min.
So, Vyom takes 1/2 min for every step.
For 20 steps, he takes 20/2 min, i.e. 10 min.
Difference between their times = 1.66 min
Escalator moves 5 steps (i.e. 25 steps of Shyam - 20 steps of Vyom) in 1.66 min.
Speed of escalator is 1 step for 0.33 min, i.e. 3 steps per minute (same as that of Shyam).
If escalator is moving, Shyam takes 25 steps and escalator also takes 25 steps.
Hence, total number of steps to be taken when escalator was turned off = 50.
Hence, option (b).
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