CAT Question Bank - Escalators (Time, Speed & Distance)
AP & HP concept can be used
Since the speeds are in AP, time taken will be in HP = 2 * 30 * 70/100 = 42
Let escalator moves "a" steps in case of Sam and "b" steps in case of john.
(Note : Escalator will move different no of steps in both the case as time taken will be different)
Let the number of steps required when escalator is stopped be "x".
30 + a = x --(1)
70 - b = x --(2)
30 + a = 70 - b --(3)
Now, Speed of both Sam and John is same.
So, If they take equal steps, then the escalator will also take equal step.
When Sam takes 30, Escalator takes "a" steps
=> Sam takes 210, Escalator takes 7a
When John takes 70, Escalator takes "b" steps
=> John takes 210, Escalator takes 3b
(Common Ratio : 210)
Hence, 7a = 3b --(4)
Solve(3) and (4), a = 12
Hence, x =42
[Credits : Akshay Kumar]
Q2) A uses an escalator at the railway station. If A runs up 8 steps of the escalator, then it takes him 37.5 seconds to reach the top of the escalator. If he runs up 14 steps of the escalator, then it takes him only 28.5 seconds to reach the top. How many seconds would it take A to reach the top if he did not run up any steps of the escalator at all?
8 + n(37.5) = 14 + (28.5)n
6 = 9n
n = 2/3
so steps= 8 + 2/3 * 375/10 = 8 + 25 = 33
so 33 * 3/2= 49.5 seconds
[credits - @swetabh_kumar]
Q3) Ravi is climbing on a moving escalator that is going up and takes 30 steps to reach the top. Rakesh on the other hand is coming down on the same escalator. For every 5 steps that Rakesh takes, Ravi takes only 3 steps. Both of them take the same amount of time to reach the other end.
a) What is the total number of steps in the escalator?
b) What is the difference in the number of steps that both of them had taken when they crossed each other?
Let us assume their speeds are 5s and 3s, and the speed of the escalator is 'x'
Since both of them take the same time for the same distance, their effective speed is the same.
=> 5s - x = 3s + x
=> x = s
Speed of Ravi : Speed of escalator = 3s : s = 3 : 1
=> When Ravi takes 30 steps, the escalator takes 10 steps.
=> Total number of steps = 30 + 10 = 40 steps.
Both of them would have covered 20 steps when they crossed each other.
Ravi going up would have taken 15 steps, whereas the escalator would have taken 5 steps for him.
Rakesh coming down would have taken 25 steps, out of which the escalator would have nullified the movement of 5 steps for him.
Difference in the number of steps = 25 - 15 = 10
[credits : Biswanath Chakraborty]
Q4) Raju is walking down an escalator which is moving down. From the top, he takes 20 steps to reach the bottom. While Rajat, who walks twice as fast as Raju, takes 30 steps from the top to reach the bottom. Find the number of steps that Rajesh, a friend of Raju, would take to reach the bottom, if he starts from the top and walks half fast as Raju.
Q5) Shyama and Ramesh walk up an escalator which moves at a constant speed. Shyama takes three steps for every two of Ramesh’s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Ramesh (because his slower pace lets the escalator do a little more of the work) takes 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?
Q6) An escalator is moving at 3 steps per second. Harish walks in the same direction as moving escalator at 2 steps per second takes 3 second less to get out of the escalator than when he was moving on the stationary escalator. How many steps are there in the stationary escalator?
When moving with escalator
Steps covered per sec = 3 + 2 = 5
when moving in stationary escalator
steps covered per sec = 2
Let the total steps = X
X/2 - X / 5 = 3
X = 10
[credits: Abhishek Dangayach]
Q7) Mr. Perumal decided to walk down the escalator of a tube station. He found that if he walks 26 steps, he requires 30 s to reach the bottom. However, if he walks 34 steps he would only require 18 s to reach to the bottom. If the escalator is moving downwards, find the number of steps in the escalator
26 + 30e = 34 + 18e
12e = 8
e = 2/3
26 + 20 = 46
Q8) Mohit moves with a constant speed of 3 steps/second and Sonal moves with a constant speed of 1 step/second on an escalator. When the escalator moves downward at a constant speed, Mohit takes 90 steps while Sonal takes 60 steps to reach the bottom from the top of the escalator. How many steps would be visible in the escalator when it becomes stationary?
Q9) A woman is walking down a downward moving escalator and steps down 10 steps to reach the bottom. Just as she reaches the bottom a sale commences on the floor above. She runs back up on the downward moving escalator at a speed five times that which she walked down. She covers 25 steps in reaching the top. How many steps are visible on the escalator when it is switched off ?
We have given his speeds
so let his earlier speed be 1 step/minute and speed of escalator be x.
So time taken to walk 10 steps is 10 mins
Case 1) 10 + 10x
Case 2) His speed increases by 5 times so new speed becomes 5 steps/ min and time taken is 5 mins
25 - 5x
10 + 10x = 25 - 5x
x = 1
total stairs = 20
[Credits : Shweta Arora]
Q10) Rahul & Ajay walk up an escalator which is moving at a constant speed. Rahul takes 2 steps for every 4 steps of Ajay. Ajay takes 20 steps while Rahul takes 12 steps to reach the top. Find how many visible steps are there on the staircase?
20 + 5e = 12 + 6e
e = 8
Total steps = 20 + 5 x 8 = 60
Q11) A man can walk up in a moving escalator in 30 s. The same man can walk down this moving up escalator in 90s. Assume that this walking speed is sane both upwards and downwards. How much time will he take to walk up the escalator when it is not moving ?
Shyama = 3
Ramesh = 2
25 + 25e/3 = 20 + 10e
e = 3
Total steps : 20 + 10 x 3 = 50
Speed of man = x steps/min,
Speed of escalator = n steps/min up only.
In 30 secs,
Total steps upward = (x+n)/2 steps
In 90 secs downwards = (x-n)*3/2 steps
These two steps count should be equal.
x = 2n
Time taken= 45 secs
[credits: Rohit Kumar Pandey]
Q12) A person, A, starts descending from the first floor of a building to the ground floor on a descending escalator, while another person, B, simultaneously starts ascending from the ground floor of the building to the first floor, using the same escalator. If the speed of B is twice that of A, and A and B take 30 steps and 120 steps to reach their respective destinations, find the number of steps that are visible on the escalator when it is stationary.