Escalator questions have now become one of the most frequented questions in the competitive exams. Similarly, 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 these questions more effectively. By being able to solve the escalator questions, candidates can easily score well in the CAT quantitative aptitude section.
What are Escalator Questions?
Escalator questions are very similar to the upstream and downstream questions. In a stream, the direction of flow of water is constant whereas, the escalators move in both directions. Escalator questions can be confusing as sometimes, questions might not explicitly reveal the direction in which the escalator is moving.
Types of Escalator Questions:
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.
Example Questions on Escalators:
Ramu takes 40 seconds to walk up on an upward moving escalator but he takes 60 seconds to walk up on a downward moving escalator. Calculate the time that Ramu will take to walk up if the escalator is not moving?
This question resembles boats and streams questions a lot. It can be solved using the same concept.
Assume speed of Ramu as “x” and speed of 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.
When Ramu walks down, he takes 1 minute on an escalator which 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?
Assume the speed of the escalator to be “a” steps per second.
As it is an escalator, distance covered by Ramu will always be 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.
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 step Suresh took. What was the total number of steps in that escalator?
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.
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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