Meeting again at the start on a circular track: On a 5 km circular track, A, B, and C start together in the same direction at 2.5 km/h, 3 km/h, and 2 km/h, respectively. After how many hours will all three meet again at the starting point?

Introduction / Context:
When multiple runners set off on a circular track, they are all back at the start together at the least common multiple (LCM) of their individual lap times.

Given Data / Assumptions:

• Track length = 5 km.
• Speeds: 2.5, 3, and 2 km/h; constant speeds.

Concept / Approach:
Compute lap periods: T1 = 5/2.5 = 2 h; T2 = 5/3 = 5/3 h; T3 = 5/2 = 2.5 h. The required time is LCM(T1, T2, T3).

Step-by-Step Solution:

Verification / Alternative check:
LCM via integerizing denominators also yields 10 h.

Why Other Options Are Wrong:
6/15/30 are common distractors but fail integrality for at least one runner.

Common Pitfalls:
Using arithmetic mean or max instead of LCM of lap periods.

Final Answer:
10 hours