CAT Question Bank  Escalators (Time, Speed & Distance)

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?

@ASHISH
Speed of escalator (n) = 2/3 steps/seconds
Number of steps = 33 steps
Time = Distance/Speed = 33 / (2/3) = 33 * 3/2 = 49.5 seconds.

@rowdyrathore
no of steps=75
time taken=45 sec