CAT 2022 Question Paper | Quant Slot 1

CAT Questions

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 6 : Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is

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Video Explanation

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Explanatory Answer

Let the meeting point of the two trains between stations X and Y be M.
Let the time taken to reach M from X by train A be ‘t’ minutes. Since the two trains start simultaneously, the time taken by train B to reach M from Y will also be ‘t’ minutes.
We know that train A completes the entire journey in 10 minutes, so the time taken by train A to travel from M to Y will be ‘10 - t’ minutes. We are told that train B takes 9 minutes to reach X after it meets train A, which means, train B takes 9 minutes to travel from M to X.
When two bodies travel equal distances at constant speeds, the ratio of time taken by them to travel those distances will be the same.
The time taken by A and B to travel the distance between A and M is ‘t’ minutes and 9 minutes respectively. Similarly, the time taken by them to travel the distance between M and B is ‘10 - t’ and ‘t’ minutes.
The ratio of the times taken should be equal.
\(\frac{t}{9}=\frac{10-t}{t}\)
\(t^2=9(10-t)\)
\(t^2=90-9 t\)
\(t^2+9 t-90=0\)
\(t^2+15 t-6 t-90=0\)
\(t(t+15)-6(t+15)=0\)
\((t+15)(t-6)=0\)
t = - 15 or t = 6
t can’t be negative, therefore, t is 6.
The total time taken by train B to reach station X from station Y is 6 + 9 =
15 minutes.

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The answer is '15'

Choice A is the correct answer.