Shivam is climbing on a moving escalator that is going up and takes 30 steps to reach the top. Atharva on the other hand is coming down on the same escalator. For every 5 steps that Atharva takes, Shivam takes only 3 steps. Both of them take the same amount of time to reach the other end. What is the difference in the number of steps that both of them had taken when they crossed each other?
Explanation:
Let us assume their speeds are 5s and 3s, and the speed of the escalator is 'x'.
Since both of them take the same time for the same distance, their effective speed is the same.
⇒ 5s - x = 3s + x
⇒ x = s
Speed of Shivam : Speed of escalator = 3s : s = 3 : 1
⇒ When Shivam takes 30 steps, the escalator takes 10 steps.
⇒ Total number of steps = 30 + 10 = 40 steps.
Both of them would have covered 20 steps when they crossed each other.
Shivam going up would have taken 15 steps, whereas the escalator would have taken 5 steps for him.
Atharva coming down would have taken 25 steps, out of which the escalator would have nullified the movement of 5 steps for him.
Difference in the number of steps = 25 - 15 = 10 steps.
Hence, 10.
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