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The question is from the topic Races. It discusses about three people with different speeds running around a cirucular track. It is a classic question involving the concept of speed, distance and ratios. Time Speed and Distance is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 4: Three friends A, B and C decide to run around a circular track. They start at the same time and run in the same direction. A is the quickest and when A finishes a lap, it is seen that C is as much behind B as B is behind A. When A completes 3 laps, C is the exact same position on the circular track as B was when A finished 1 lap. Find the ratio of the speeds of A, B and C?

  1. 5 : 4 : 2
  2. 4 : 3 : 2
  3. 5 : 4 : 3
  4. 3 : 2 : 1

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Explanatory Answer

Method of solving this CAT Question from Races: Think about the distance covered by each individual at a point of time and anchor the question around it.

Let track length be equal to T. When A completes a lap, let us assume B has run a distance of (t - d). At this time, C should have run a distance of (t - 2d).

After 3 laps C is in the same position as B was at the end of one lap. So, the position after 3t - 6d should be the same as t - d. Or, C should be at a distance of d from the end of the lap. C will have completed less than 3 laps (as he is slower than A), so he could have traveled a distance of either t - d or 2t - d.

=> 3t - 6d = t - d
=> 2t = 5d
=> d = 0.4t

The distances covered by A, B and C when A completes a lap will be t, 0.6t and 0.2t respectively. Or, the ratio of their speeds is 5 : 3 : 1.

In the second scenario, 3t - 6d = 2t - d => t = 5d => d = 0.2t.

The distances covered by A, B and C when A completes a lap will be t, 0.8t and 0.6t respectively. Or, the ratio of their speeds is 5 : 4 : 3.

The question is " Find the ratio of the speeds of A, B and C?"
The ratio of the speeds of A, B and C is either 5 : 3 : 1 or 5 : 4 : 3.

Hence, the answer is 5 : 4 : 3

Choice C is the correct answer.


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