There is a escalator and 2 persons move down it.A takes 50 steps and B takes 75 steps while the escalator is moving down.Given that the time taken by A to take 1 step is equal to time taken by B to take 3 steps.Find the no. of steps in the escalator while it is staionary?	Options:
A) 60 B) 70 C) 80 D) 90 E) 100

Rationale: if a takes 1 step in one second , then b takes 3 steps in one second . if a takes t 1 seconds to take 50 steps , then b takes 150 steps in t 1 seconds . for b , to take 150 steps he requires t 1 seconds , then to take 75 steps he requires t 1 / 2 seconds . now use relative velocity l - v * t 1 = 50 ( for first person ) l - v * t 1 / 2 = 75 ( for second person ) s ( escalator w . r . t ground ) - s ( person w . r . t escalator ) = s 1 ( person w . r . t ground ) s , s , s 1 are the steps now put the v * t 1 from 1 into the second equation and u get l - ( l - 50 ) / 2 = 75 l + 50 = 150 l = 100 answer : e
Answer: E