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You walk upwards on an upwards moving escalator, with a speed of 1 step/ second. After 50 steps you are at the upper floor. You turn around and run downwards on the same escalator, with a speed of 5 steps/ second. After 125 steps you are back at the bottom landing of the escalator. How many steps are there in the escalator, when it stands still?
Correct answer is '100'. Can you explain this answer?
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Most Upvoted Answer
You walk upwards on an upwards moving escalator, with a speed of 1 st...
Given information:
- The person walks upwards on an upwards moving escalator with a speed of 1 step/second.
- After 50 steps, the person reaches the upper floor.
- The person then turns around and runs downwards on the same escalator with a speed of 5 steps/second.
- After 125 steps, the person is back at the bottom landing of the escalator.
Let's assume:
- The speed of the escalator is 'e' steps/second.
- The total number of steps in the escalator is 's'.
Analysis:
When the person walks upwards on the escalator:
- The effective speed is the sum of their walking speed and the speed of the escalator. So, (1 + e) steps/second.
- The person covers 50 steps in total. Therefore, the time taken to cover 50 steps is 50/(1 + e) seconds.
When the person runs downwards on the escalator:
- The effective speed is the difference between their running speed and the speed of the escalator. So, (5 - e) steps/second.
- The person covers 125 steps in total. Therefore, the time taken to cover 125 steps is 125/(5 - e) seconds.
Equations:
From the given information, we can form the following equations:
1. Time taken upwards = Time taken downwards
2. 50/(1 + e) = 125/(5 - e)
Solving the equation:
Cross-multiplying equation 2, we get:
50(5 - e) = 125(1 + e)
250 - 50e = 125 + 125e
175e = 125 + 250
175e = 375
e = 375/175
e = 2.14 (approximately)
Conclusion:
The speed of the escalator is approximately 2.14 steps/second. Since the speed of the escalator cannot be fractional, we can assume it to be 2 steps/second.
To find the total number of steps in the escalator, we substitute the value of 'e' in equation 2:
50/(1 + 2) = 125/(5 - 2)
50/3 = 125/3
solving for s,
s = 125
Therefore, there are 125 steps in the escalator when it stands still.
- The person walks upwards on an upwards moving escalator with a speed of 1 step/second.
- After 50 steps, the person reaches the upper floor.
- The person then turns around and runs downwards on the same escalator with a speed of 5 steps/second.
- After 125 steps, the person is back at the bottom landing of the escalator.
Let's assume:
- The speed of the escalator is 'e' steps/second.
- The total number of steps in the escalator is 's'.
Analysis:
When the person walks upwards on the escalator:
- The effective speed is the sum of their walking speed and the speed of the escalator. So, (1 + e) steps/second.
- The person covers 50 steps in total. Therefore, the time taken to cover 50 steps is 50/(1 + e) seconds.
When the person runs downwards on the escalator:
- The effective speed is the difference between their running speed and the speed of the escalator. So, (5 - e) steps/second.
- The person covers 125 steps in total. Therefore, the time taken to cover 125 steps is 125/(5 - e) seconds.
Equations:
From the given information, we can form the following equations:
1. Time taken upwards = Time taken downwards
2. 50/(1 + e) = 125/(5 - e)
Solving the equation:
Cross-multiplying equation 2, we get:
50(5 - e) = 125(1 + e)
250 - 50e = 125 + 125e
175e = 125 + 250
175e = 375
e = 375/175
e = 2.14 (approximately)
Conclusion:
The speed of the escalator is approximately 2.14 steps/second. Since the speed of the escalator cannot be fractional, we can assume it to be 2 steps/second.
To find the total number of steps in the escalator, we substitute the value of 'e' in equation 2:
50/(1 + 2) = 125/(5 - 2)
50/3 = 125/3
solving for s,
s = 125
Therefore, there are 125 steps in the escalator when it stands still.
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Community Answer
You walk upwards on an upwards moving escalator, with a speed of 1 st...
Let N = no. of steps in escalator (when escalator is stand-still), and E = Speed of the escalator
When walking upwards on the escalator, Speed = 1 step/ second. Number of steps taken = 50
N / (E + 1) = 50/1... (1)
When walking downwards on the escalator, Speed = 5 step/ second, but now he is running against the direction of the escalator, Number of steps taken = 125
N/ (5 - E) = 125/5 ... (2)
Solving (1) by (2) , we get E = 1 and N = 100 steps.
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You walk upwards on an upwards moving escalator, with a speed of 1 step/ second. After 50 steps you are at the upper floor. You turn around and run downwards on the same escalator, with a speed of 5 steps/ second. After 125 steps you are back at the bottom landing of the escalator. How many steps are there in the escalator, when it stands still?Correct answer is '100'. Can you explain this answer?
Question Description
You walk upwards on an upwards moving escalator, with a speed of 1 step/ second. After 50 steps you are at the upper floor. You turn around and run downwards on the same escalator, with a speed of 5 steps/ second. After 125 steps you are back at the bottom landing of the escalator. How many steps are there in the escalator, when it stands still?Correct answer is '100'. 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 You walk upwards on an upwards moving escalator, with a speed of 1 step/ second. After 50 steps you are at the upper floor. You turn around and run downwards on the same escalator, with a speed of 5 steps/ second. After 125 steps you are back at the bottom landing of the escalator. How many steps are there in the escalator, when it stands still?Correct answer is '100'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for You walk upwards on an upwards moving escalator, with a speed of 1 step/ second. After 50 steps you are at the upper floor. You turn around and run downwards on the same escalator, with a speed of 5 steps/ second. After 125 steps you are back at the bottom landing of the escalator. How many steps are there in the escalator, when it stands still?Correct answer is '100'. Can you explain this answer?.
You walk upwards on an upwards moving escalator, with a speed of 1 step/ second. After 50 steps you are at the upper floor. You turn around and run downwards on the same escalator, with a speed of 5 steps/ second. After 125 steps you are back at the bottom landing of the escalator. How many steps are there in the escalator, when it stands still?Correct answer is '100'. 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 You walk upwards on an upwards moving escalator, with a speed of 1 step/ second. After 50 steps you are at the upper floor. You turn around and run downwards on the same escalator, with a speed of 5 steps/ second. After 125 steps you are back at the bottom landing of the escalator. How many steps are there in the escalator, when it stands still?Correct answer is '100'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for You walk upwards on an upwards moving escalator, with a speed of 1 step/ second. After 50 steps you are at the upper floor. You turn around and run downwards on the same escalator, with a speed of 5 steps/ second. After 125 steps you are back at the bottom landing of the escalator. How many steps are there in the escalator, when it stands still?Correct answer is '100'. Can you explain this answer?.
Solutions for You walk upwards on an upwards moving escalator, with a speed of 1 step/ second. After 50 steps you are at the upper floor. You turn around and run downwards on the same escalator, with a speed of 5 steps/ second. After 125 steps you are back at the bottom landing of the escalator. How many steps are there in the escalator, when it stands still?Correct answer is '100'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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ample number of questions to practice You walk upwards on an upwards moving escalator, with a speed of 1 step/ second. After 50 steps you are at the upper floor. You turn around and run downwards on the same escalator, with a speed of 5 steps/ second. After 125 steps you are back at the bottom landing of the escalator. How many steps are there in the escalator, when it stands still?Correct answer is '100'. Can you explain this answer? tests, examples and also practice CAT tests.
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