CAT 2021 Slot 2 · Quant · Question 5

CAT 2021 Slot 2 previous year question on Time Speed and Distance, with the answer and a step-by-step solution.

Time Speed and DistanceArithmeticMultiple choiceMedium
Two trains A and B were moving in opposite directions, their speeds being in the ratio 5 : 3. The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other. It took another 69 seconds for the rear ends of the trains to cross each other. The ratio of length of train A to that of train B is
  1. A
    2:3
  2. B
    2:1
  3. C
    5:3
  4. D
    3:2
Pick an option, then check.
Answer & solution

Answer: Option D

Work entirely in relative terms. Moving in opposite directions, the gap between the trains closes at the relative speed v=5k+3k=8k, which is constant throughout.

Start the clock when the front ends cross. For the front of A to reach the rear of B, the pair must close exactly the length of B, so {L}_{B}=46v.

For the rear ends to cross, the pair must close both lengths together, and that happens at 46+69=115 seconds, so {L}_{A}+{L}_{B}=115v.

Therefore {L}_{A}=115v-46v=69v, and {L}_{A}:{L}_{B}=69:46=3:2.

Note that the speed ratio 5 : 3 is never needed; only the relative speed matters.

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