Page and Plant are running on a track AB of length 10 metres. They start running simultaneously from the ends A and B respectively. The moment they reach either of the ends, they turn around and continue running. Page and Plant run with constant speeds of 2m/s and 5m/s respectively. How far from A (in metres) are they, when they meet for the 23^rd time?

Solution(By Examveda Team)

The ratio of speeds is 2 : 5. So when slower one completes 2 one way journeys (and reaches its starting point), faster one travels 5 one way journeys (and reaches the other end). So that means after the faster one has traveled 5 one way journeys, both of them have reached same end and in next 5 one-way journey of faster runner, both reach their starting position simultaneously. Now most important to observe is that FASTER one will always meet the SLOWER one EXACTLY ONCE in each of its one-way journey, except when both of them have started with the same starting point.
Once you reduce that for the 5^th time, they'll meet at A, and the next 5 rounds will have 4 meetings.
Then, just add 5 + 4 + 5 + 4 + 5 = 23 or just go by the position of Plant after every 5 rounds : A, B, A, B, A. The cycle repeats.
So, total distance will be 0 meters.