Question { iNautix, 25503 }

Mr. Shah decided to walk down the escalator of a tube
station. He found that if he walks down 26 steps, he
requires 30seconds toreach the bottom. However, if he steps
down 34 stairshe would onlyrequire 18 seconds to get to the
bottom. If the timeis measured fromthe moment the top step
begins to descend to thetime he steps offthe last step at
the bottom, find out the height ofthe stair way in steps?

Answer

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