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There is an escalator that goes up from the ground floor to the first floor . Mahesh walks up the escalator at a uniform speed. On reaching the first floor, he immediately turns back and walks down the same escalator at the same speed and returns to the ground floor. He completes the to to and fro movement in 80 seconds. If Mahesh doubles his speed, he will be able to finish the to and fro movement in only 32 seconds. What is the ratio of the speed of Mahesh to to the speed of the escalator?
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There is an escalator that goes up from the ground floor to the first ...
Problem Statement:
There is an escalator that goes up from the ground floor to the first floor. Mahesh walks up the escalator at a uniform speed. On reaching the first floor, he immediately turns back and walks down the same escalator at the same speed and returns to the ground floor. He completes the to and fro movement in 80 seconds. If Mahesh doubles his speed, he will be able to finish the to and fro movement in only 32 seconds. What is the ratio of the speed of Mahesh to the speed of the escalator?
Understanding the Problem:
We need to determine the ratio of Mahesh's speed to the speed of the escalator. Mahesh walks up and down the escalator, completing a round trip in 80 seconds at his original speed, and in 32 seconds at twice his original speed. We need to find the ratio of these speeds.
Let's assume:
Let the speed of Mahesh be M units per second and the speed of the escalator be E units per second.
Key observations:
1. When Mahesh walks up the escalator, his effective speed is the sum of his speed and the speed of the escalator.
2. When Mahesh walks down the escalator, his effective speed is the difference between his speed and the speed of the escalator.
3. The distance covered by Mahesh in one direction is the same as the distance covered by the escalator in the opposite direction.
Calculating the speed:
Let's calculate the time taken by Mahesh to go up the escalator and come down at his original speed:
- Time taken to go up the escalator: Distance/Speed = 1/M-E
- Time taken to come down the escalator: Distance/Speed = 1/M+E
According to the given information, the total time taken for the round trip is 80 seconds:
1/M-E + 1/M+E = 80
Similarly, when Mahesh doubles his speed, the total time taken for the round trip is 32 seconds:
1/2M-E + 1/2M+E = 32
Solving the equations:
We have two equations with two variables (M and E). By solving these equations simultaneously, we can find the values of M and E.
Let's simplify the equations by finding the least common multiple (LCM) of the denominators:
(2M-E + 2M+E)/((2M-E)(2M+E)) = 32/80
4M/((4M)^2-E^2) = 2/5
(4M)^2-E^2 = 5 * 4M
16M^2 - E^2 = 20M
E^2 = 16M^2 - 20M
E^2 = 4M(4M - 5)
E = 2√(M(4M - 5))
By substituting this value of E in the equation 1/M-E + 1/M+E = 80, we can solve for M.
Finding the ratio:
Once we find the values of M and E, we can calculate the ratio of Mahesh's speed to the speed of the escalator:
Ratio = Mahesh's speed/Escalator's speed = M/E
There is an escalator that goes up from the ground floor to the first floor. Mahesh walks up the escalator at a uniform speed. On reaching the first floor, he immediately turns back and walks down the same escalator at the same speed and returns to the ground floor. He completes the to and fro movement in 80 seconds. If Mahesh doubles his speed, he will be able to finish the to and fro movement in only 32 seconds. What is the ratio of the speed of Mahesh to the speed of the escalator?
Understanding the Problem:
We need to determine the ratio of Mahesh's speed to the speed of the escalator. Mahesh walks up and down the escalator, completing a round trip in 80 seconds at his original speed, and in 32 seconds at twice his original speed. We need to find the ratio of these speeds.
Let's assume:
Let the speed of Mahesh be M units per second and the speed of the escalator be E units per second.
Key observations:
1. When Mahesh walks up the escalator, his effective speed is the sum of his speed and the speed of the escalator.
2. When Mahesh walks down the escalator, his effective speed is the difference between his speed and the speed of the escalator.
3. The distance covered by Mahesh in one direction is the same as the distance covered by the escalator in the opposite direction.
Calculating the speed:
Let's calculate the time taken by Mahesh to go up the escalator and come down at his original speed:
- Time taken to go up the escalator: Distance/Speed = 1/M-E
- Time taken to come down the escalator: Distance/Speed = 1/M+E
According to the given information, the total time taken for the round trip is 80 seconds:
1/M-E + 1/M+E = 80
Similarly, when Mahesh doubles his speed, the total time taken for the round trip is 32 seconds:
1/2M-E + 1/2M+E = 32
Solving the equations:
We have two equations with two variables (M and E). By solving these equations simultaneously, we can find the values of M and E.
Let's simplify the equations by finding the least common multiple (LCM) of the denominators:
(2M-E + 2M+E)/((2M-E)(2M+E)) = 32/80
4M/((4M)^2-E^2) = 2/5
(4M)^2-E^2 = 5 * 4M
16M^2 - E^2 = 20M
E^2 = 16M^2 - 20M
E^2 = 4M(4M - 5)
E = 2√(M(4M - 5))
By substituting this value of E in the equation 1/M-E + 1/M+E = 80, we can solve for M.
Finding the ratio:
Once we find the values of M and E, we can calculate the ratio of Mahesh's speed to the speed of the escalator:
Ratio = Mahesh's speed/Escalator's speed = M/E
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There is an escalator that goes up from the ground floor to the first floor . Mahesh walks up the escalator at a uniform speed. On reaching the first floor, he immediately turns back and walks down the same escalator at the same speed and returns to the ground floor. He completes the to to and fro movement in 80 seconds. If Mahesh doubles his speed, he will be able to finish the to and fro movement in only 32 seconds. What is the ratio of the speed of Mahesh to to the speed of the escalator?
Question Description
There is an escalator that goes up from the ground floor to the first floor . Mahesh walks up the escalator at a uniform speed. On reaching the first floor, he immediately turns back and walks down the same escalator at the same speed and returns to the ground floor. He completes the to to and fro movement in 80 seconds. If Mahesh doubles his speed, he will be able to finish the to and fro movement in only 32 seconds. What is the ratio of the speed of Mahesh to to the speed of the escalator? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There is an escalator that goes up from the ground floor to the first floor . Mahesh walks up the escalator at a uniform speed. On reaching the first floor, he immediately turns back and walks down the same escalator at the same speed and returns to the ground floor. He completes the to to and fro movement in 80 seconds. If Mahesh doubles his speed, he will be able to finish the to and fro movement in only 32 seconds. What is the ratio of the speed of Mahesh to to the speed of the escalator? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There is an escalator that goes up from the ground floor to the first floor . Mahesh walks up the escalator at a uniform speed. On reaching the first floor, he immediately turns back and walks down the same escalator at the same speed and returns to the ground floor. He completes the to to and fro movement in 80 seconds. If Mahesh doubles his speed, he will be able to finish the to and fro movement in only 32 seconds. What is the ratio of the speed of Mahesh to to the speed of the escalator?.
There is an escalator that goes up from the ground floor to the first floor . Mahesh walks up the escalator at a uniform speed. On reaching the first floor, he immediately turns back and walks down the same escalator at the same speed and returns to the ground floor. He completes the to to and fro movement in 80 seconds. If Mahesh doubles his speed, he will be able to finish the to and fro movement in only 32 seconds. What is the ratio of the speed of Mahesh to to the speed of the escalator? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There is an escalator that goes up from the ground floor to the first floor . Mahesh walks up the escalator at a uniform speed. On reaching the first floor, he immediately turns back and walks down the same escalator at the same speed and returns to the ground floor. He completes the to to and fro movement in 80 seconds. If Mahesh doubles his speed, he will be able to finish the to and fro movement in only 32 seconds. What is the ratio of the speed of Mahesh to to the speed of the escalator? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There is an escalator that goes up from the ground floor to the first floor . Mahesh walks up the escalator at a uniform speed. On reaching the first floor, he immediately turns back and walks down the same escalator at the same speed and returns to the ground floor. He completes the to to and fro movement in 80 seconds. If Mahesh doubles his speed, he will be able to finish the to and fro movement in only 32 seconds. What is the ratio of the speed of Mahesh to to the speed of the escalator?.
Solutions for There is an escalator that goes up from the ground floor to the first floor . Mahesh walks up the escalator at a uniform speed. On reaching the first floor, he immediately turns back and walks down the same escalator at the same speed and returns to the ground floor. He completes the to to and fro movement in 80 seconds. If Mahesh doubles his speed, he will be able to finish the to and fro movement in only 32 seconds. What is the ratio of the speed of Mahesh to to the speed of the escalator? in English & in Hindi are available as part of our courses for CAT.
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