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?  Choose one: A) 5 : 4 : 2 B) 4 : 3 : 2 C) 5 : 4 : 3 D) 3 : 2 : 1 E) None of these
DETAILED SOLUTION   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 three laps C would have traveled a distance of 3 * (t - 2d) = 3t - 6d.   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.   =&gt; 3t - 6d = t - d   =&gt; 2t = 5d   =&gt; 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 =&gt; t = 5d =&gt; 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 ratio of the speeds of A, B and C is either 5 : 3 : 1 or 5 : 4 : 3.   5 : 4 : 3orrect Answer: 5 : 4 : 3
<result>C</result>
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?