# Mr. Shah decided to walk down the escalator of a tube station. He found that if he walks down 26 steps, he requires 30 seconds to reach the bottom. However, if he steps down 34 stairs he would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way in steps?

#### sarapriti Profile Answers by sarapriti

• May 24th, 2008

Let the speed of escalator be x steps/sec

then total steps in escalator is  26 + 30x (since the escalator covers 30x steps while the person covers 26 steps)

Similarly the in the second case the total no of steps is 34 + 18x

solving both ..  26 + 30x = 34 + 18x

12x = 8  , x = 2/3 therefore steps is 26 + 30*2/3 = 46 steps

#### krishnna

• Aug 25th, 2011

46

#### Shubham Takode

• Jul 27th, 2015

In 12 sec(30-18) he walks down 8(34-26) steps.
therefore, (8*30)/12 =20 steps.
So, the total height of the stair way in steps=(26+20)=46 steps

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