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?

Consider pondering the distances covered by each individual at a specific juncture and framing the inquiry around this notion.

Let’s designate the track length as T. When A completes a lap, let’s suppose B has traversed a distance of (T – d). At that moment, C ought to have covered a distance of (T – 2d).

After three laps, C finds themselves in the same position that B occupied at the culmination of one lap. Therefore, the position after 3T – 6d should mirror T – d. Hence, C should be positioned at a distance of d from the end of the lap. Given that C is slower than A, C will have completed fewer than three laps, allowing for the possibility of having 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. Thus, the ratio of their speeds is 5:3:1.

In the alternate 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. Thus, the ratio of their speeds is 5:4:3.

The query is “Determine the ratio of the speeds of A, B, and C?” The ratio of their speeds can either be 5:3:1 or 5:4:3. Consequently, the answer is 5:4:3.

Option C is the correct answer.