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# Escalator

Posted on 2006-03-23
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An escalator is moving down. A person who comes down with normal speed, takes 50 steps to come down. Another person, who is slightly faster, takes 90 steps to come down. The time taken by the first person to move 10 steps is the same as the time taken by the second person to move 90 steps.

What is the total number of steps visible when the escalator is not moving ?

Note: The faster person takes more steps because, if you don't move at all, you take 0 steps and you come down, and your speed is still slower !
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Question by:Harisha M G

LVL 33

Assisted Solution

We'll call the 50-step person A, and the 90-step person B.

Let the number of steps be x.
Let the elevator move at n steps per second.
For person A, the elevator moves x - 50 steps.  The whole trip takes (x - 50) / n seconds.
For person B, the elevator moves x - 90 steps.  The whole trip takes (x - 90) / n seconds.
Person A's trip takes 5 times longer than person B's trip.
ergo,
(x - 50) / n = 5 * (x - 90) / n
x - 50 = 5x - 450
400 = 4x
x = 100
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LVL 37

Author Comment

Yeah, I thought it so, but the answer given is 150..

Any ideas ? or is it wrong ?
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LVL 4

Expert Comment

snoyes_jw:  Your equation negates the impact of the speed of the escalator.  Is it possible that the speed of the escalator is relevant?  Common sense seems to dicate that it would be, but your math seems good.
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LVL 33

Expert Comment

If the speed of the escalator mattered, it would need to be provided in the the question to produce an answer.  It isn't given, so it must not matter.
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LVL 16

Accepted Solution

Hi Harish!

I think this is just a more drivvelled version of snoyes_jw's one but:

If escalator has 150 steps and escalator moves at x seconds per step -

In 50 steps for person A, escalator has moved 150-50=100 steps and therefore takes 100x seconds.
Person A took 50 steps in that time so walked at a speed of 50/100x steps/second or 100x/50 seconds/step so 10 steps would take 1000x/50 or 20x seconds.
In 90 steps for person B, escalator has moved 150-90=60 steps and therefore takes 60x seconds.
Person B took 90 steps in that time so walked at a speed of 90/60x steps/second or 60x/90 seconds/step so 90 steps would take 5400x/90 or 60x seconds.

Different! Therefore either 150 is wrong or I am wrong - probably the latter.

For an n-step escalator:

In 50 steps for person A, escalator has moved n-50 steps and therefore takes (n-50)x seconds.
A took 50 steps in that time so walked at a speed of 50/(n-50)x steps/second or (n-50)x/50 seconds/step so 10 steps would take (n-50)x/5 seconds.
In 90 steps for person B, escalator has moved n-90 steps and therefore takes (n-90)x seconds.
B took 90 steps in that time so walked at a speed of 90/(n-90)x steps/second or (n-90)x/90 seconds/step so 90 steps would take (n-90)x seconds.

So

(n-90)x = (n-50)x/5   (and x IS therefore irrelevant)

or

5n - 450 = n - 50 -> 4n = 400 -> n = 100

The book loses?

Paul
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LVL 3

Assisted Solution

Slower person's speed is  x steps per sec and
Faster person's speed is 9x steps per sec

Slower took total 50 steps
so time taken = 50/x

Faster took total 90 steps
so time taken = 90/9x = 10/x

Time taken ratio]

slower:Faster
5:1

now for this time escalator moved with constant speed so
moved step ratio by escalator in case of slower and faster will be
5:1

so steps can be

5k and k

totals steps for slower = 5k + 50
totals steps for faster = k + 90

so

5k + 50 = k + 90

5k = k = 90 - 50

k = 10

so Total steps are 5k + 50 or k + 90

so answer is 100
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LVL 37

Author Comment

Thank you all for confirming my answer :)

Is there any chance that the problem is worded badly and it should have been something else, so that the answer comes to be 150 ?

It is not a problem given in book, it was asked in an interview !
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LVL 33

Expert Comment

Perhaps the point of the question is more about your confidence in your own results, and your tact in asserting the the interviewer is wrong...
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LVL 12

Assisted Solution

Perhaps they messed up and the time it takes the first person to move 10 steps is the time it takes the 2nd person to move 30 steps? If you're taking 9 steps in the time someone else takes 1, I don't think you're "slightly faster"; you're way faster.

(x - 50) = 5/3 * (x-90)
x - 50 = 5/3x - 150
100 = 2/3x
x = 150
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LVL 37

Author Comment

Thanks for all of your answers. Here is the original question:
http://aucse.com/infosys-sample%20paper%204.htm

I am increasing the points and splitting..
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