In a subway station, there is a long escalator.

Question

In a subway station, there is a long escalator. Two brothers have to get to a baseball game and are in a hurry, and so they run up the moving steps, adding their speed to that of the escalator. The taller boy climbs three times as quickly as his little brother, and while he runs up he counts 75 steps. The little one counts only 50. How many steps does the visible part of this escalator have?

A. 50
B. 75
C. 100
D. 150
E. 200

A. 50
B. 75
C. 100
D. 150
E. 200

chetan2u · Accepted Answer

This is more of a puzzle than a GMAT question, but it is always good to test your reasoning abilities.

Two ways.

Purely logical

Speed of elder brother is thrice, so younger would have taken 75/3 or 25 steps when the elder brother reaches top.

This means there are 75-25 or  50 steps  between the top and younger brother.

But we know that younger takes a total of 50 steps to reach top, so he will take another 25 steps in the remaining  50 steps  that are between him and top. 
Then who does the remaining 25 steps of these  50 steps ?: it is the escalator. So escalator does 25 and younger brother does 25 in last  50 steps .

So escalator does 1 step for each step of younger brother or 50 steps for 50 steps of younger brother. 
Total steps = 50 of escalator + 50 of younger brother =100 steps

chetan2u · Answer

Algebraic way

Let the total steps be n. 
Ratio of speed of E:Y= 3:1, and steps taken to reach top = 75:50 
Ratio of time taken by each brother to cover 75:50 steps at a ratio of speed of 3:1 = 75/3:50/1=25:50=1:2
So steps done by escalator in each case = n-75:n-50, but the time taken should also be the same as time taken by the two brothers, that is 1:2. 
Because the escalator takes the same amount to assist the brothers to reach top. For example, if elder brother takes 60 seconds to take 75 steps, the escalator also takes 60 seconds to cover n-75 steps.

Thus,  \frac{n-75}{n-50}=\frac{1}{2} 
 2n-150=n-50.......n=100

C

udaypratapsingh99 · Answer

That's an excellent approach.

My approach was,

We know that n number of steps disappeared for the elder brother because of escalators speed. Thus for his brother, who's running at 66% lower speed, 2n must have disappeared. Thus, there required number is 50+2*(75-50) = 100

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In a subway station, there is a long escalator.

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