Concept of Esclator

In this article we will cover the questions based on the concept of esclator. Once you are through with the concept of Esclator then you will be able to solve all the questions from this topic. Problems on escalator use the concept of Time, Speed and Distance. But we need to keep certain things in mind:

1) The distance is in terms of the number of steps in the esclator/stairs.
Let 'n' be the number of steps in the esclator.
2) Individual is moving in the same direction as that of the escalator.
i + e = n where 'i' are the number of steps taken by the individual and 'e' are the number of steps taken by the escalator Incase, the Individual is moving in the opposite direction as that of the escalator. It will be the subtraction of 'e' and 'i' The time taken by the individual to climb up or down the escalator is equal to the time for which escalator is moving.

Type of questions that can be asked.
1) Calculate the number of steps of the escalator.
2) Calculate the speed of escalator.
3) Calculate the steps taken by the person/escalator.
Now let's consider some questions to understand the concept.

Read More: CAT 2013

Q1) Karan climbs 13 stairs in the same time as Arjun climbs 9 stairs. If Arjun starts climbing the stairs 5 seconds before Karan starts climbing them, Karan reached the top of the staircase 3 seconds before Arjun. However, if both of them start climbing the stairs simultaneously Karan reaches the top 36 stairs ahead of Arjun. What is the number of stairs in the staircase?

1) 52
2) 98
3) 117
4) None of these

Read More: CAT 2014 LR sets

Solution:
Easiest way to solve problems based on Esclators is to read the question carefully and atart forming equations as per the information specified in the question.
Say Karan climbs a stair in 1/x seconds whereas, Arjun climbs a stair in 1/y seconds.
As, Karan climbs 13 stairs in the same time as Arjun climbs 9 stairs. So, 13/x = 9/y i.e. 13y = 9x ---Equation 1
According to the question, n/y = n/x + 8 where 'n' is the total number of stairs in the staircase.
n(x - y) = 8xy ---Equation 2
If both of them start climbing the stairs simultaneously Karan reaches the top 36 stairs ahead of Arjun.
n/x = (n - 36)/y i.e. n(x - y) = 36x ---Equation 3
From Equation 2, 3
8xy = 36x i.e. y = 4.5
Put y = 4.5 in Equation 1.
13(4.5) = 9x i.e. x = 6.5
Put x = 6.5, y = 4.5 in Equation 3.
n(6.5 - 4.5) = 36(6.5) i.e. n = 117
Hence, Option 3.

Read More: CAT 2015 LR sets

Q2) Two persons are climbing up on two moving esclators which have 120 steps. The ratio of 1st person's speed to that of the 1st esclator is 2:3 (steps). The ratio of 2nd person's speed to that of the 2nd esclator is 3:5 (steps). The total number of steps taken by both ther persons are 1) 85
2) 93
3) 80
4) 75

Solution:
Ratio of 1st person's speed to that of the 1st esclator is 2:3 i.e. for every 2 steps taken by the person esclator moves 3 steps.
Total steps taken by 1st person = (120)2/5 = 48
Ratio of 2nd person's speed to that of the 2nd esclator is 3:5 i.e. for every 3 steps taken by the person esclator moves 5 steps.
Total steps taken by 1st person = (120)3/8 = 45
The total number of steps taken by both ther persons are 48 + 45 = 93
Hence, Option 2.