CAT Question Bank - Escalators (Time, Speed & Distance)
Let escalator moves up with a speed of E steps per sec and man moves with a speed of 1 step per sec
when both are moving up
S = (E+1)
T = 30
So D = 30 (E+1)
Now when man moves down on up moving escalator
T = 90
on solving E = 1/2 steps per sec
Q14) Two persons A and B are walking down an escalator in the direction of the motion of the escalator. The ratio of the speeds (in steps) of A and B is 2 : 1 respectively. A covers 60 steps to get out of the escalator and B takes 40 steps to do the same. Find the number of steps in the escalator when it is stationary?
When A takes 60 steps, let Escalator takes x steps.
Total no. of steps on a stionary esc = x + 60.
so B will take 30 Steps since Speed is half.
So when B takes 40 steps Escalator should take 4/3x steps.
4/3x + 40 = x+60 and hence x = 60
Ans = 120
Q15) There is an escalator going up from the ground floor to the first floor. Raghu is climbing up the escalator while Rajan is climbing down (from the first floor to the ground floor) on the same escalator. On a stationary escalator, the time taken by Rajan to climb 8 steps is same as the time taken by Raghu to climb 6 steps. On the moving escalator, if Raghu takes 18 steps to reach the first floor while Rajan takes 60 steps to reach the ground floor, how many steps are there on the escalator?
d-18/t1 = (60-d)/t2
60/t2/(18/t1) = 4/3
hence t1/t2= 2/5
so 5d - 90= 120 - 2d
so 7d = 210
d = 30
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Q16) An escalator is coming down at a constant speed . Vivek takes 40 steps to reach to the bottom .The time in which he takes 15 steps , Samar manages to reach the bottom by taking 45 steps .If the escalator were turned off, how many steps would they have to take to walk down?
n is speed of escalator.
so steps of escalator= n(40/v) = n * time in which vivek takes 40 steps
no. of steps = 40 + n(40/v) = 45 + n(45/3v)
3v since samar covers 45 steps by the time vivek covers 15 steps.
5 = 25n/v
so n/v = 1/5
so steps=40 + 40n/v
= 40 + 40 * 1/5
Q17) A man wants to go to the first floor of the building. He can either go from an escalator which is going up to the first floor or from an escalator which is coming down from the first floor. He takes 40 steps if he goes up with an escalaor going up and 160 steps if he goes up with an escalator coming down. The speed of both the escalators is same. Find out the number of steps on an escalator
If e is the speed of escalator and s is man's speed.
40 + (e/s) * 40 = 160 - (e/s) * 160
e/s = 3/5
thus total steps = 40 + (3/5) * 40 = 64
Q18) An escalator is descending at constant speed. A walks down and takes 50 steps to reach the bottom. B runs down faster and takes 90 steps to reach the bottom.If B takes 90 steps in the same time as A takes 10 steps then how many steps are visible when the escalator is not operating?
50 + (5e/9) * 9 = 90 + e
40 = 4e
e = 10
Ans = 90 + 10 = 100
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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
N/4x - e = 154/4x = 100
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
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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?
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.
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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
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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) = 30-n(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
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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/5-e = 125/5 = 25
solving we get e = 1 ; N = 100
Approach 2 (preferred approach for escalators)
N = 50 + 50e = 125 - 25e
solving we get e = 1 , N =100
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?