CAT Question Bank  Escalators (Time, Speed & Distance)

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

@rowdyrathore 46 steps

@badalravi Correct!
Let's suppose that escalator moves n steps/sec.
It is given that if he walks he takes 30 sec and covers 26 steps.
So in that 30 sec escalator would have covered 30n steps.
Hence the total number of steps on the escalator is 26 + 30n  (1)
Similarly when he runs he takes 18 sec and covers 34 steps.
So in 18 sec escalator covers 18n steps.
Hence total steps on the escalator must be 34 + 18n  (2)
Equating (1) & (2) 26 +30n = 34 + 18n we get n = 2/3
Hence no. steps is 26 + 30(2/3) = 46.[Solved by Priya]

@badalravi Please check once.
Day 1 mohit takes 20/1 = 20 seconds
Day 2 mohit takes 32/2 = 16 seconds
Distance covered is same
if e is the speed of escalator,
20 x (1 + e) = 16 x (2 + e)
20 + 20e = 32 + 16e
4e = 12
e = 3 steps/sec
Total number of steps = 20 x 4 = 80 steps ?

@rowdyrathore why did you multiplied by 3/2 in the last?