CAT 2022 Question Paper | Quant Slot 3

CAT Previous Year Paper | CAT Quant Questions | Question 12

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 12 : 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

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Explanatory Answer

When Moody walks for 30s, let the steps rolled out by the escalator be 3x and the steps walked by Moody be 3y.
Therefore, when the escalator runs for only 20s, the steps rolled out by the escalator equals 2x. Since Moddy is also spending only 20s instead of 30s on the escalator, but walking at double the speed, he walks 4y steps.

Steps rolled by the Escalator
Steps walked by Moody
Total Steps
(Length of Escalator)
3x + 3y
2x + 4y
The total steps of the escalator remain the same in both scenarios.
3x + 3y = 2x + 4y
x = y
Total length of the escalator = 3x + 3y = 6x
When Moody doesn’t walk on the Escalator, the Escalator has to roll out all the 6x steps for him.
Since the Escalator takes 30s to roll out 3x steps, it would take 60s to roll out all the 6x steps.

The answer is '60'

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