Along a circular running track, P can complete 5 rounds in 40 minutes. Time taken by R to complete 7 rounds is equal to time taken by P to complete 6 rounds. If they start running in the same direction from two different ends of a diameter, then they will meet for the first time after ____ minutes.

Correct option is C

Given
P completes 5 rounds in 40 minutes.
Time for R to do 7 rounds = Time for P to do 6 rounds.
They run in the same direction from opposite ends of a diameter.
Formula Used
Speed = $$\frac{\text{Distance}}{\text{Time}}$$​​
Time to meet =  $$\frac{\text{Initial Distance}}{\text{Relative Speed}}$$​​
Solution
Let the track length be L.
Speed of P = $$\frac{5L}{40} = \frac{L}{8}$$​per minute.
Time taken by P to complete 6 rounds =$$\frac{6L}{L/8}$$​= 48 minutes.
R completes 7 rounds in 48 minutes, so Speed of R =$$\frac{7L}{48}$$​per minute.
Initial distance between them = 0.5L (since they start at opposite ends of a diameter).
Relative speed (same direction) = Speed of R - Speed of P
Relative speed = $$\frac{7L}{48} - \frac{L}{8} = \frac{7L - 6L}{48} = \frac{L}{48}$$​ per minute.

Time to meet = $$\frac{0.5L}{L/48} = 0.5 \times 48$$​ = 24 minutes.
Final Answer
So the correct answer is (c) 
Exam Hall Method:
They start at opposite ends of a diameter, meaning the initial gap between them is exactly 0.5 rounds.