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An escalator is moving up. Rohit and his girlfriend walk up the moving escalator. Rohit has a walking speed one and half times that of his girlfriend. Rohit reaches the top after taking 40 steps, while his girlfriend does so after taking 30 steps. If the escalator is switched off, how many steps would Rohit take to walk up to the top?
Correct answer is '120'. Can you explain this answer?
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Verified Answer
An escalator is moving up. Rohit and his girlfriend walk up the moving...
Let the walking speed of Rohit be 1.5x and that of his girlfriend be x. Let the speed of the escalator be S steps/unit time, and the number of steps on the escalator be N.
As per information provided for Rohit, we can say that N = (40/1.5x) * (1.5x+S)
As per information provided for Rohit's girlfriend, N = (30/x) * (x+S)
Equating the two we get S = 3x
Hence number of steps on the escalator is N = 120.
As per information provided for Rohit, we can say that N = (40/1.5x) * (1.5x+S)
As per information provided for Rohit's girlfriend, N = (30/x) * (x+S)
Equating the two we get S = 3x
Hence number of steps on the escalator is N = 120.
Most Upvoted Answer
An escalator is moving up. Rohit and his girlfriend walk up the moving...
Given information:
- Rohit takes 40 steps to reach the top while walking up the moving escalator.
- His girlfriend takes 30 steps to reach the top while walking up the moving escalator.
- Rohit's walking speed is one and a half times that of his girlfriend's walking speed.
To find:
- Number of steps Rohit would take to walk up to the top when the escalator is switched off.
Assumptions:
- The escalator's speed is constant and not given.
- The escalator's speed is not affected by the weight of Rohit and his girlfriend.
- The escalator's speed is the same for both Rohit and his girlfriend.
Solution:
Let's assume the girlfriend's walking speed is x steps per second. Therefore, Rohit's walking speed is 1.5x steps per second.
Calculating Time:
The time taken by Rohit to reach the top = 40 steps / (1.5x steps/second) = 40/(1.5x) seconds
The time taken by the girlfriend to reach the top = 30 steps / (x steps/second) = 30/x seconds
Calculating the Relative Speed:
When Rohit walks up the moving escalator, his effective speed is the sum of his walking speed and the escalator's speed.
Let's assume the escalator's speed is y steps per second.
Therefore, the relative speed of Rohit = 1.5x + y steps per second
Similarly, the relative speed of the girlfriend = x + y steps per second
Calculating the Distance:
Rohit takes 40 steps to reach the top, so the distance covered by Rohit = 40 steps
Similarly, the distance covered by the girlfriend = 30 steps
Calculating the Time:
The time taken by Rohit to reach the top = Distance / Relative Speed = 40 / (1.5x + y) seconds
The time taken by the girlfriend to reach the top = Distance / Relative Speed = 30 / (x + y) seconds
Since both Rohit and his girlfriend take the same time to reach the top, we can equate the two equations:
40 / (1.5x + y) = 30 / (x + y)
Simplifying the Equation:
Cross-multiplying the equation gives us:
40(x + y) = 30(1.5x + y)
40x + 40y = 45x + 30y
Simplifying further:
40y - 30y = 45x - 40x
10y = 5x
2y = x
Calculating Rohit's Steps:
When the escalator is switched off, the relative speed becomes the walking speed of Rohit, which is 1.5x steps per second.
Let's assume the number of steps Rohit takes to reach the top without the escalator is n.
Therefore, the time taken by Rohit to reach the top without the escalator = n / (1.5x) seconds
Since the distance covered by Rohit without the escalator is the same as before (40 steps), we can equate the two equations:
n / (
- Rohit takes 40 steps to reach the top while walking up the moving escalator.
- His girlfriend takes 30 steps to reach the top while walking up the moving escalator.
- Rohit's walking speed is one and a half times that of his girlfriend's walking speed.
To find:
- Number of steps Rohit would take to walk up to the top when the escalator is switched off.
Assumptions:
- The escalator's speed is constant and not given.
- The escalator's speed is not affected by the weight of Rohit and his girlfriend.
- The escalator's speed is the same for both Rohit and his girlfriend.
Solution:
Let's assume the girlfriend's walking speed is x steps per second. Therefore, Rohit's walking speed is 1.5x steps per second.
Calculating Time:
The time taken by Rohit to reach the top = 40 steps / (1.5x steps/second) = 40/(1.5x) seconds
The time taken by the girlfriend to reach the top = 30 steps / (x steps/second) = 30/x seconds
Calculating the Relative Speed:
When Rohit walks up the moving escalator, his effective speed is the sum of his walking speed and the escalator's speed.
Let's assume the escalator's speed is y steps per second.
Therefore, the relative speed of Rohit = 1.5x + y steps per second
Similarly, the relative speed of the girlfriend = x + y steps per second
Calculating the Distance:
Rohit takes 40 steps to reach the top, so the distance covered by Rohit = 40 steps
Similarly, the distance covered by the girlfriend = 30 steps
Calculating the Time:
The time taken by Rohit to reach the top = Distance / Relative Speed = 40 / (1.5x + y) seconds
The time taken by the girlfriend to reach the top = Distance / Relative Speed = 30 / (x + y) seconds
Since both Rohit and his girlfriend take the same time to reach the top, we can equate the two equations:
40 / (1.5x + y) = 30 / (x + y)
Simplifying the Equation:
Cross-multiplying the equation gives us:
40(x + y) = 30(1.5x + y)
40x + 40y = 45x + 30y
Simplifying further:
40y - 30y = 45x - 40x
10y = 5x
2y = x
Calculating Rohit's Steps:
When the escalator is switched off, the relative speed becomes the walking speed of Rohit, which is 1.5x steps per second.
Let's assume the number of steps Rohit takes to reach the top without the escalator is n.
Therefore, the time taken by Rohit to reach the top without the escalator = n / (1.5x) seconds
Since the distance covered by Rohit without the escalator is the same as before (40 steps), we can equate the two equations:
n / (
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An escalator is moving up. Rohit and his girlfriend walk up the moving escalator. Rohit has a walking speed one and half times that of his girlfriend. Rohit reaches the top after taking 40 steps, while his girlfriend does so after taking 30 steps. If the escalator is switched off, how many steps would Rohit take to walk up to the top?Correct answer is '120'. Can you explain this answer?
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An escalator is moving up. Rohit and his girlfriend walk up the moving escalator. Rohit has a walking speed one and half times that of his girlfriend. Rohit reaches the top after taking 40 steps, while his girlfriend does so after taking 30 steps. If the escalator is switched off, how many steps would Rohit take to walk up to the top?Correct answer is '120'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about An escalator is moving up. Rohit and his girlfriend walk up the moving escalator. Rohit has a walking speed one and half times that of his girlfriend. Rohit reaches the top after taking 40 steps, while his girlfriend does so after taking 30 steps. If the escalator is switched off, how many steps would Rohit take to walk up to the top?Correct answer is '120'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An escalator is moving up. Rohit and his girlfriend walk up the moving escalator. Rohit has a walking speed one and half times that of his girlfriend. Rohit reaches the top after taking 40 steps, while his girlfriend does so after taking 30 steps. If the escalator is switched off, how many steps would Rohit take to walk up to the top?Correct answer is '120'. Can you explain this answer?.
An escalator is moving up. Rohit and his girlfriend walk up the moving escalator. Rohit has a walking speed one and half times that of his girlfriend. Rohit reaches the top after taking 40 steps, while his girlfriend does so after taking 30 steps. If the escalator is switched off, how many steps would Rohit take to walk up to the top?Correct answer is '120'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about An escalator is moving up. Rohit and his girlfriend walk up the moving escalator. Rohit has a walking speed one and half times that of his girlfriend. Rohit reaches the top after taking 40 steps, while his girlfriend does so after taking 30 steps. If the escalator is switched off, how many steps would Rohit take to walk up to the top?Correct answer is '120'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An escalator is moving up. Rohit and his girlfriend walk up the moving escalator. Rohit has a walking speed one and half times that of his girlfriend. Rohit reaches the top after taking 40 steps, while his girlfriend does so after taking 30 steps. If the escalator is switched off, how many steps would Rohit take to walk up to the top?Correct answer is '120'. Can you explain this answer?.
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