CAT Quantitative Ability Questions | CAT TIme, Speed, Distance and Work questions
CAT/2001
Question . 101
Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom’s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?
Explanatory Answer
Method of solving this CAT Quantitative Ability Question from TIme, Speed, Distance and Work question
(b) If Shyama takes 1 minutes for every 3 steps, then she takes 1/3 minutes for every step.
For 25 steps, he takes 25/3 minutes = 8.33 minutes. So, Vyom takes 1/2 minutes for every step.
For 20 steps, he takes 10 minutes.
Difference between their times = 1.66 minutes
Escalator takes 5 steps in 1.66 minutes.
Speed of escalator is 1 step for 0.33 minutes = 3 steps per minutes.
If escalator is moving, then Shyam takes 25 steps and escalator also takes 25 steps.
Hence, total number of steps = 50.