# Escalator Problems (Solved) - Vikas Saini

• There are 3 cases in escalator

1. When escalator is stationary.
2. Escalator is moving upwards.
3. Escalator is moving downwards.

If my speed is ‘a’ and speed of escalator is ‘b’.

When escalator is moving upwards
(i) If you are moving upwards then total speed = a+b.
(ii) If you are moving downwards then total speed = |a-b|.

When escalator is moving downwards
(i) If you are moving upwards then total speed = |a-b|.
(ii) If you are moving downwards then total speed = a+b.

There is an escalator is moving upwards. You take 8 seconds to take up & 10 seconds when escalator is not moving. Speed of escalator is 2 step/sec.

formula d = st.
8 (a+2) = 10a.
8a+16 = 10a
a = 8.
Total steps = 8(a+2) = 10a = 80 step.

Raju takes 40 seconds to walk up on an escalator which is moving upwards but he takes 60 seconds to walk up on an escalator which is moving downwards. How much time will he take to walk up if the escalator is not moving?

Suppose Ravi’s speed = a.
Escalator’s speed = b.
By formula d = st.
(a+b)40 = (a-b)60
2a + 2b = 3a – 3b.
a = 5b.
Total steps = (5b+b)40 = 240b.
Time he will take when escalator is stationary = 240b / 5b = 48 seconds.

Rohit 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?

Speed of escalator is a.
Rohit whether runs or walks, distance must be same.
20 + 60a = 30+40a
20a = 10.
a = 1/2.
Steps = 20 + 60 x (1/2) = 50.

Ravi and Rakesh are climbing on a moving escalator that is going up. Ravi takes 10 seconds to reach the top but Rakesh takes 8 seconds to reach the top. This happens because Rakesh is faster than Ravi. Rakesh takes 4 steps whereas Ravi can take only 3 steps in one second. What is the total number of steps in the escalator?

Suppose speed of escalator =a.
(a+4)8 = (a+3)10.
a = 1.
Total steps = (1+4)8 = 40.

A and B are climbing on a moving escalator that is going up. A takes 30 steps to reach the top whereas B takes 32 steps for the same. This happens because B is faster than A. For every 4 steps that B takes, A takes only 3 steps. What is the total number of steps in the escalator?

A takes time =30/3 = 10.
B takes time = 32/4 = 8.
Suppose speed of escalator is a.
10(a+3) = 8(a+4)
a = 1.
Total steps = 10(1+3) = 40.

A man can walk up a moving up escalator in 30 seconds. The same can walk down this moving up escalator in 90 seconds. How much time he will take when escalator is stationary ?

Man’s speed is a and escalator speed is b.
(a+b)30 = (a-b)90
a = 2b.
Total steps = 90b.
Time taken by him = 90b / 2b = 45 seconds.

A and B speed ratio is 2:3. The steps taken by A & B are 25 & 30 at climbing escalator. When A is walking up and B is walking down then after how many steps B will take to meet A ?

Time taken by A = 25/2 = 12.5 seconds.
Time taken by B = 30/3 = 10 seconds.
Speed of escalator is a.
(2+a) 12.5 = (3+a)10
25 + 12.5a = 30 +10a
a = 2.
Total steps = (3+2)10 = 50.
Steps taken by B = 50 x 3 / (3+2) = 30 steps.

A & B walk up an escalator (moving stairway), the escalator moves at a constant speed. A takes 3 steps for every 2 steps of B. A gets to the top of the escalator having taken 25 steps, while B takes only 20 steps to reach the top. If the escalator were turned off. How many steps would they have to take up ?

Time taken by A = 25/3.
Time taken by B = 20/2 = 10.
Let speed of escalator = a.
(a+2)10 = (a+3)25/3
30a + 60 = 25a + 75.
a = 3.
Total steps = (3+2)10 = 50.

On an upward moving escalator A, B, C take 10,8,5 steps respectively to reach the top. A takes 30 step to come down on same moving up escalator. Find the time ratio by B & C.

Let speed of A = 1step/sec.
Speed of escalator = a.
10(1+a) = 30(1-a)
10 + 10a = 30 – 30a
a = 1/2
Total steps = 10 ( 1+1/2) = 15.
B takes time = 15-8 = 7.
C takes time = 15-5 = 10.
Time ratio = 7:10

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