Overtaking time with staggered starts: Arun starts from P at 6:00 am at 8 km/h. Bhaskar starts from P at 7:30 am at 12 km/h, both running in the same direction. At what time does Bhaskar overtake Arun?

Introduction / Context:
Overtaking with different start times uses relative speed and initial lead distance acquired before the faster runner starts.

Given Data / Assumptions:

• Arun: 8 km/h from 6:00 am.
• Bhaskar: 12 km/h from 7:30 am (1.5 h later).
• Same route and direction; constant speeds.

Concept / Approach:
Lead distance at 7:30 am is d = 8 * 1.5 = 12 km. Relative speed = 12 − 8 = 4 km/h. Catch time after 7:30 am is d / relative speed.

Step-by-Step Solution:

Verification / Alternative check:
Distances by 10:30 am: Arun = 4.5 h * 8 = 36 km; Bhaskar = 3 h * 12 = 36 km – same point.

Why Other Options Are Wrong:
9:00/11:30 do not satisfy both distances equally; 1:00 am is nonsensical in this context.

Common Pitfalls:
Forgetting to compute Arun’s initial lead before Bhaskar starts.

Final Answer:
10 : 30 am