Two runners A and B start running from diametrically opposite points on a circular track in the same direction. If A runs at a constant speed of 8 km/h and B at a constant speed of 6 km/h and A catches up with B in 30 minutes, what is the length of the track?

Correct option is D

Given:

• Speeds:
  A = 8 km/h
  B = 6 km/h
• A and B start from diametrically opposite points on a circular track, running in the same direction
• A catches up with B in 30 minutes = 0.5 hours

Concept Used:

When two people move in the same direction, their relative speed = Difference of their speeds.

A has to cover half the track more than B to catch up, since they start from opposite ends.

Solution:

Relative speed = A’s speed – B’s speed = 8 – 6 = 2 km/h

Time to catch up = 0.5 hours

So, distance between them initially (on circular track) = Relative Speed × Time
= 2 × 0.5 = 1 km

Since they start from diametrically opposite points, this is half the track.

So, Full track length = 2 × 1 = 2 km

Final Answer: (d) 2 km