Train M leaves Meerut at 6:00 a.m. and reaches Delhi at 10:00 a.m. Train D leaves Delhi at 8:00 a.m. and reaches Meerut at 11:30 a.m. At what time do they cross?

Introduction / Context:
Two trains depart from opposite ends at different start times and travel times. Let the meet time be t hours after the first train starts; write a distance-balance equation using their constant speeds.

Given Data / Assumptions:

• Meerut→Delhi: 6:00 to 10:00 → 4 h.
• Delhi→Meerut: 8:00 to 11:30 → 3.5 h.
• Constant speeds; same distance D.

Concept / Approach:
Speeds: v1 = D/4, v2 = D/3.5. If they meet t hours after 6:00, train 2 has traveled (t − 2) hours (for t ≥ 2). Total distance covered at meet equals D.

Step-by-Step Solution:
D = (D/4)*t + (D/3.5)*(t − 2).Divide by D: 1 = t/4 + (t − 2)/3.5.Solve → t = 44/15 h ≈ 2.933.. h after 6:00 → 8:56 a.m.

Verification / Alternative check:
Check distances: v1*t = D*(t/4); v2*(t − 2) = D*((t − 2)/3.5). Their sum equals D by construction.

Why Other Options Are Wrong:
Other times do not satisfy the proportionality with the given end-to-end durations.

Common Pitfalls:
Using the average of departure times or travel times instead of solving the linear equation.

Final Answer:
8:56 a.m.