CAT Question Bank  Escalators (Time, Speed & Distance)

Q19) Nitin walked up a descending escalator and took 154 steps in 100 seconds to reach top. Rahul started from top taking 3 steps for every 4 steps taken by Nitin and reaches the bottom in 40 sec. How many steps from bottom were they when they crossed each other?

Let their speeds be 3x and 4x
For Nitin
N/4x  e = 154/4x = 100
For Rahul
N/3x + e = 40
Equating we get N = 77 (total steps)
And putting this value in any one equation, we get x = 77/200
Now, they will meet in time 77/4x + 3x = 200/7 seconds
Distance covered by Nitin from the bottom in this time = (4x  e) * 200/7 = 22
[Credits : Aanya singh]

Q20) There were two escalators in a mall, with the same number of steps, the first one moving up and the second moving down at the same speed. Ram and Sameer walk up the first escalator at their respective uniform speeds. Ram took 2 steps in the time that Sameer took one. Ram and Sameer reached the top of the escalator after taking 30 steps and 20 steps respectively. Ram then started to walk down the second escalator. At the same time, Tarun started to walk up the second escalator at twice Ram’s speed. How many steps would Tarun take before meeting Ram?

Method 1:
Let the speed of Ram be 1 step per second.
Then speed of sameer = 0.5 steps per second.
Let the speed of the escalator be x steps per second.
Total time taken by Ram = 30 secs (as he takes 30 steps to reach the top at the rate of 1 step per sec).
So, total steps = 30 + 30x
Total time taken by Sameer = 40 secs.
So, total steps = 20 + 40x
so 30 + 30X = 20 + 40X
So, x = 1, So, total steps = 60 and speed of escalator = 1 step per sec.Now, on the second escalaor, Ram walks down at 2 steps per sec (Relative speed).
Tarun climbs up at 1 steps per sec (2 * 1 (speed of Tarun)  1 (speed of escalator).
So, relative speed of Tarun and Ram = 2 + 1 = 3 steps/sec and hence total time = 60/3= 20 sec.
So, in 20 secs Tarun walks 20 * 2=40 steps.
[Credits : Abhishek varma]Method 2:
Ram  2 steps/min
Shyam  1 step/min
30 + 15e = 20 + 20e
e = 2 step/min
2nd escalator = 2 + e = 4 step/min
Shyam= 4  e = 2 step
So total steps = 60
So 60 = 40 : 20
So 20/2 = 10 * 4 = 40 steps
[Credits: Sandeep Patra]

Q21) You walk upwards on an escalator with a speed of 1 step/sec. After 50 steps, you are at the end. You turn around and run downwards at a speed of 5 steps/sec. After 125 steps, you are back at the beginning of the escalator. How many steps do you need if escalator stands still ?

Q22) On an upward moving escalator Amit, Sanjeev and Vicky take 10 steps, 8 steps and 5 steps respectively to reach the top. On the same upward moving escalator Amit takes 30 steps to come down from the top. Find the ratio of the time taken by Sanjeev and Vicky to reach the top.
a. 7 : 16
b. 8 : 5
c. 5 : 8
d. 7 : 10

for amit, 10+n (10/v) = 30n(30/v)
n/v = 1/2
so steps = 10+10*1/2 = 15
8+nTs = 15 so nTs =7 n=speed of esc, Ts= speed of sanjeev
5+nTv =15 so nTv = 10 Tv = speed of vicky.
so ratio = 7:10
[credits : @swetabh_kumar]

Approach 1
let the total no. of steps in escalator be N and speed of escalator be "e" steps per sec
so N/(1 + e) = 50
and N/5e = 125/5 = 25
solving we get e = 1 ; N = 100Approach 2 (preferred approach for escalators)
N = 50 + 50e = 125  25e
solving we get e = 1 , N =100[credits: @sibanand_pattnaik]

Q23) Jordan wanted to climb down from the first floor to the ground floor of a shopping mall, whereas Karina wanted to climb up from the ground floor to the first floor. Both use the same escalator which was ascending from the ground floor to the first floor and both walked their respective destinations. Both of them started simultaneously from the top and the bottom of the escalator respectively and crossed each other after exactly 21 seconds. If instead, Karina had walked at 1/3rd of his speed while Jordan maintained his speed, they would have crossed each other after exactly 28 seconds from the start. Further if both Jordan and Karina had climbed up from the ground floor to the first floor using the same ascending escalator, the number of steps taken by Karina to reach the first floor would be 20% less than the number of steps taken by Jordan for the same. If Jordan were to stand still on the same escalator, how long would it take for the escalator to take him from the ground floor to the first floor?

Q24) Mohit walks up an upgoing escalator at the rate of one step per second. Twenty steps bring him to the top. The next day he goes up at two steps per second, reaching the top in 32 steps. How many steps are there in the escalator?

Q25) In an escalator moving from first floor to the ground floor in a shopping mall, Ram observed that , it took him 30 seconds to reach the ground floor if he took 25 steps but if he tripled his speed it took him only 18 seconds.
How many steps escalator has ? (steps visible when escalator is stationary)
Also, if Ram didn't travel on his own and only the elevator was in motion, what would be the time taken for him to reach the ground floor from the first floor?

Q26) A and B are running up an ascending escalator. B runs 3 times as fast as A. In all, B climbs 45 steps in reaching the top while A climbs only 24 steps. If escalator is switched off, how many steps would be visible ?

Q27) Ram takes 60 seconds on an escalator which is moving down when he walks down but takes 40 seconds when he runs down. He takes 20 steps when he walking whereas he takes 30 steps when he is running. What is the total number of steps in the escalator?

Q28) Atul and Mahesh are climbing on a moving escalator that is going up. Atul takes 30 steps to reach the top whereas Mahesh takes 32 steps for the same. Mahesh takes 4 steps whereas Atul can take only 3 steps in one second. What is the total number of steps in the escalator?

Q29) Two guys A and B are walking down an escalator in the direction of the motion of the escalator. A takes three steps in the same Time when B takes two steps. When A covers 90 steps he gets out of the escalator while B takes 80 steps to get out of the escalator. If they start from opposite ends using the same escalator, find the difference in steps covered by them when they meet.
(a) 48
(b) 20
(c) 30
(d) 24

Q30) A person walking takes 26 steps to come down on a escalator and it takes 30 seconds for him for walking. The same person while running takes 18 second and 34 steps. How many steps are there in the escalator?

Raju = 1 steps/second
Rajat = 2 steps/second
Escalator = E steps/second
Now Raju takes 20 steps
So 20(1+E)
Similarly, Rajat takes 15 seconds
15(2+E)
Now 20(1+E) = 15(2+E)
=> 5E = 10
=> E = 2 steps/second
Total number of steps = 20(1+2) = 60
And now Rajesh speed = (1/2) steps/second
So time taken by Rajesh
= 60/(2+1/2) = 24 seconds
So Rajesh steps = 1/2 (24) = 12 steps[credits : @LearnQuest]
Alternative:
Raju/E = 20/(n20)
Rajat/E = 30/(n30)
Raju/Rajat = 1/2 = 2/3*(n30)/(n20)
3n60 = 4n120
n= 60
Now Rajesh/Raju = 1/2 = x/(60x)*40/20
x=12
[Credits : Srinjoy Ghosh]

@rowdyrathore let x step/sec of mohits speed
(20/x) + (20/1) = (32/x)+(32/1)
X = 1/3 steps /second
Total steps = 20 * 3 = 60 steps

@rowdyrathore b speed =3x
A speed = x
Let e be escalators speed
45+(45/3)e = 24 + 24e
E = 7/3
Steps = 45 +15×7/3 = 90 steps

@rowdyrathore 24 steps
A=3steps/seconds
B=2steps/seconds
(90+90e/3)= 80+(80e/2)
E= 1
N= 120 steps
Time wen they meet = 24 secs
Steps covered = 24*(32) = 24