CAT 2022 Slot 3 QA Q12 Time, Speed & Distance

Question 12 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.

Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is

TITA: type in the answer. There are no options and no negative marking.

Answer: 60 Time, Speed & Distance TITA

Solution

  1. Let walking speed \(w\), escalator speed \(e\), length \(L\).
  2. \(L=30(w+e)=20(2w+e)\Rightarrow 30w+30e=40w+20e\Rightarrow e=w\).
  3. \(L=30\cdot2e=60e\), so standing still takes 60 seconds.

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