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Raju is walking down an escalator (a moving staircase) which is moving down. From the top, he takes 20 steps to reach the bottom, while Rajat, who walks twice as fast as Raju, takes 30 steps from the top to reach the bottom.Question No. 11DIRECTIONS for questions 11 and 12: Type in your answer in the input box provided below the question.Find the total number of steps visible at any point of time on the escalator.

Question

Raju is walking down an escalator (a moving staircase) which is moving down. From the top, he takes 20 steps to reach the bottom, while Rajat, who walks twice as fast as Raju, takes 30 steps from the top to reach the bottom.Question No. 11DIRECTIONS for questions 11 and 12: Type in your answer in the input box provided below the question.Find the total number of steps visible at any point of time on the escalator.

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Solution

To solve this problem, we need to understand that the speed of the escalator is constant, but the speed of Raju and Rajat is different.

Let's denote:

  • E as the speed of the escalator
  • R as the speed of Raju
  • T as the total number of steps on the escalator

From the problem, we know that Raju's speed plus the speed of the escalator equals 20 steps (R + E = 20) and Rajat's speed, which is twice as fast as Raju's, plus the speed of the escalator equals 30 steps (2R + E = 30).

We can solve these two equations to find the values of R, E, and T.

Subtract the first equation from the second to get R = 10. Substitute R = 10 into the first equation to get E = 10.

The total number of steps on the escalator is the number of steps Raju takes plus the number of steps the escalator moves in the same time, which is T = R + E = 10 + 10 = 20.

So, the total number of steps visible at any point of time on the escalator is 20.

This problem has been solved

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