In CAT, Time, Speed and Distance (TSD) is an important topic in the Quantitative Aptitude (QA) section. Escalator problems are quite common from the TSD topic. CAT Escalator problems are similar to “upstream” “downstream” problems. In a stream, the direction of the flow of water is constant whereas the escalators move in both directions. Escalator questions can be confusing as questions might not explicitly reveal the direction in which the escalator is moving.
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In CAT, escalator questions are often repeated and sometimes give a tough time to the candidates. In this article, the escalator questions are explained in detail along with solved examples to help the CAT aspirants prepare more effectively. By being able to solve the escalator questions, candidates can easily score well in the CAT quantitative aptitude section.
Escalator questions can be categorized as the following:
- Length-related questions
- Time-related questions
- Steps-related questions
- Speed-related questions
It should also be noted that escalator questions might include two different cases i.e. when 1 person is moving and when 2 persons are moving.
Let’s look at some of the escalator questions to help practice:
Q1. Ramu takes 40 seconds to walk upon an upward-moving escalator but he takes 60 seconds to walk upon a downward moving escalator. Calculate the time that Ramu will take to walk up if the escalator is not moving?
Ans. 48 seconds
This question resembles boats and streams questions a lot. It can be solved using the same concept.
Assume the speed of Ramu as “x” and the speed of the escalator as “y”.
Case 1: Escalator is Moving Upwards
In this case, Ramu’s effective speed will be = x + y
Case 2: Escalator is Moving Downwards
In this case, Ramu’s effective speed will be = x- y
Case 3: Escalator is Not Moving
At this time Ramu’s speed will simply be his actual speed i.e. x
As the distance is constant, the three speeds i.e. x + y, x, x – y will be in arithmetic progression. Now, since time is inversely proportional to speed, the time taken in each case will be in harmonic progression.
So, calculating the harmonic mean of the given time taken will give the time taken by Ramu to walk up if the escalator is not moving i.e. (2 * 40 * 60)/ (40 + 60).
So, the answer will be 48 seconds.
No. of steps (for case 1) = 40x + 40y—————–Eq. 1
No. of Steps (for case 2) = 60x + 60y—————–Eq. 2
Now, equating both these equations,
=> x = 5y.
Putting this in Eq. 1,
No. of steps = 48x.
Now, the time taken for Ramu to walk up when the escalator is stationary = 48x/x = 48 seconds.
Q2. When Ramu walks down, he takes 1 minute on an escalator that is moving down but takes 40 seconds when he runs down. He takes 20 steps when he is walking whereas he takes 30 steps when he is running. Calculate the total number of steps in the escalator?
Ans. 50 Steps
Assume the speed of the escalator to be “a” steps per second.
As it is an escalator, the distance covered by Ramu will always be the same whether he is running or walking.
Distance when Ramu is walking = 20 + 60a———–Eq. 1
Here, 60a is covered by the escalator.
Distance when Ramu is running = 30 + 40a———–Eq. 2
Again, 40a is the distance covered by the escalator.
Now, equating both the equations, obtained equation is:
20 + 60a = 30 + 40a
=> a = 0.5
So, total number of steps will be = 20 + 60 (0.5) = 50 steps.
Q3. Suresh and Mukesh are walking up on an upward-moving escalator. It took 60 steps for Suresh to reach the top whereas Mukesh took 64 steps. While moving up, Mukesh took 4 steps for every 3 steps Suresh took. What was the total number of steps in that escalator?
Ans. 80 Steps
As the ratio of their speeds are given, assume Suresh’s speed = 3x and Mukesh’s speed = 4x
Also, let the escalator’s speed = y steps per second.
When Suresh took 60 steps, the escalator had moved 60y/ 3x
So, the total number of steps = 60 + 60y / 3x————Eq. 1
When Mukesh took 64 steps, the escalator had moved 60y/ 4x
So, total number of steps = 64 + 64y / 3x————Eq. 2
Equating both the equation, it is obtained that, y = x
Now by putting this value in any of the equations, the total number of steps can be calculated.
So, Total Number of Steps = 64 + 16 = 80 steps.
Q4. A man can walk up a moving ‘up’ escalator in 30s. The same man can walk down this moving ‘up’ escalator in 90s. Assume that his walking speed is same upwards and downwards. How much time will he take to walk up the escalator, when it’s not moving?
Ans. 45 seconds
The times taken ‘with’ and ‘against’ the escalator are in the ratio 1:3. Therefore, the steps thrown out of the escalator are also in the ratio 1:3.
Also, the number of stairs that he climbs on his own will also be in the ratio 1:3. Therefore, let the stairs he climbs are L and 3L, and steps produced by the escalator be x and 3x.
Hence, L + x = 3L – 3x or L = 2x or x = L/2. Therefore total steps = L + L/2 = 3L/2. Now, time taken for L is 30s, therefore time taken for 3L/2 will be 45s.
Q5. On an upward moving escalator, Amar, Akbar and Anthony take 10 steps, 8 steps, and 5 steps, respectively, to reach the top. On the same upward moving escalator Amar takes 30 steps to come down from the top. Find the ratio of the time taken by Akbar and Anthony to reach the top.
Ans. 7: 10
Time taken by Amar to climb down 30 steps would be thrice the time taken to climb 10 steps. Therefore, if x is the number of steps thrown by the escalator when Amar climbs 10 steps, 3x would be the number of steps thrown by the escalator when he climbs 30 steps. Total number of stairs are the same.
Therefore, 30 – 3x = 10 + x or x = 5. So total number of steps = 10 + 5 = 15. For Akbar and Anthony, the steps given out by the escalator are 15 – 8 = 7 and 15 – 5 = 10. Therefore, ratio of their time = 7: 10
These were some of the basic concepts of escalator questions that can help candidates to tackle the related questions effectively in the exam. CAT aspirants can also check quantitative aptitude questions for CAT to practice different variations of questions from the different CAT topics.
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