In this article we will be covering all types of questions related to escalator. Once you are through with the concept and are able to solve the questions in this article, you can solve any question from this topic. Questions on escalator basically use the concept of Time, Speed and Distance. But we need to keep certain things in mind:
- The distance is in terms of the number of steps.
- The number of steps taken by the individual and the escalator is equal to the total number of steps on the escalator. The total number of steps will be the addition of the two in case the individual is moving in the same direction as that of the escalator. It will be the subtraction of the two in case the escalator and the individual are moving in the opposite direction.
- The time taken by the individual to climb up or down the escalator is equal to the time for which escalator is moving.
Basically, questions asked from this topic can be of the following types:
- You are asked to calculate the number of steps of the escalator.
- You asked to calculate the speed of escalator.
- You are asked to calculate the steps taken by the person/escalator.
Now that we are clear with these points, let us put this concept to use and learn the art of solving such questions.
Solved Examples
Example 1: Bunty is going up the escalator. It takes Bunty 80 seconds to walk up the escalator which is moving upwards and 120 seconds to walk up the escalator which is moving downwards. Calculate the time taken by Bunty to climb the escalator which is stationary.
Solution:
Let Bunty's speed be "a" steps per second.
Let escalator's speed be "x" steps per second.
No. of steps (N)= 80a + 80x (Since Bunty is moving upwards, 80x will be added)
No. of steps= 120a-120x (Since Bunty is moving upwards, 120x will be subtracted)
By equating the number of steps,
80a + 80x=120a-120x
a=5x
N=80a+80x= 80a+16a=96a
Time taken when the escalator is stationary= 96a/a= 96seconds.
Example 2: Bunty and Bubli are climbing on a moving escalator that is going up. Bunty takes 60 steps to reach the top but Bubli takes 64 steps to reach the top. Bunty can take 3 steps in a second while Bubli can take 4 steps in a second. Calculate the total number of steps in the escalator.
Solution:
No. of steps= 60+ (60/3)x (Since Bunty is moving in the same direction, 20x will be added)
No. of steps=64+ (64/4)x (Since Bubli is moving in the same direction, 16x will be added)
On equating the number of steps,
60+20x=64+16x
x=1 step per second
Number of steps= 60+ (20*1) =80 steps.
Till now we have solved questions in which the speeds of individuals were given. What if the actual speeds are not given? Then how will we solve the questions? Let's see.
Example 3: Bunty and Bubli are climbing on a moving escalator that is going up. Bunty takes 60 steps to reach the top but Bubli takes 64 steps to reach the top. For every 3 steps that Bunty takes Bubli takes 4 steps. Calculate the total number of steps in the escalator.
Solution:
Here, we are given the ratios of the speed and not the exact speed.
So, let's assume the speed of Bunty to be 3a and that of Bubli to be 4a.
Let escalator's speed be x steps per second.
When Bunty takes 60 steps, escalator would have moved 60x/3a steps.
Therefore, number of steps= 60+60x/3a
When Bubli takes 64 steps, escalator would have moved 64x/4a steps.
Therefore, number of steps= 64+64x/4a
On equating the number of steps, we get,
60+60x/3a = 64+64x/4a =>x/a=1
Putting this value in 64+64x/4a, we get Number of Steps= 64+16=80
Therefore, Number of Steps=80
Example 4: Bunty is climbing up the moving escalator that is going up he takes 60 steps to reach the top while Bubli is coming down the same escalator. The speed’s ratio of Bunty and Bubli is 3:5. Calculate the number of steps if it’s given that both of them take same time to reach the other end.
Solution:
Let the speed of Bunty and Bubli be 3a and 5a steps per second respectively.
Let "t" be the time taken to take a steps.
Number of steps= 3at+xt
Also, Number of steps can be written as 5at-xt
On equating the number of steps, we get
3at + xt = 5at – xt
xt=at => x=a
When Bunty takes 60 steps, escalator would have moved 60x/3a steps i.e. 60/3 = 20 steps
Therefore, the Number of Steps = 60+ (60/3a) a= 60+20=80.
For doubts, post your comments below and our experts will provide you with the solutions.
-icon.jpg?null&itok=2FjKP8-O "Chain Rule Practice Problems"){kind=icon}
