Aptitude Hack#106(9-6-19)

Question:

Mr. Das decided to walk down the escalator of a mall. He found that if he walks down
26 steps, he requires 30seconds 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 stairway insteps?

(A)46
(B)35
(C) 56
(D)55

Answer: A) 46

Explanation:

Escalator is moving with its usual speed, addition to which the person steps down. Now let us calculate the speed of escalator in terms of the number of steps elapsed at the bottom. 
Let in 1-sec number of steps elapsed is x.
 In 30 sec, the number of steps elapsed is 30x and in 18 sec is 18x. 
Addition to this the man has stepped down in order to reach earlier compared to the normal case. Thus a total number of steps elapsed in both the case is the same as the speed of escalator is constant. 
Hence according to question, steps
26 + 30x = 34 + 18x
=>x=2/3 steps

 Thus required the number of steps 
= 26 + 30x = 46 steps