Two trains run between Manipur and Dispur. Train M: Manipur→Dispur, departs 6:00 a.m., arrives 10:00 a.m. (4 h). Train D: Dispur→Manipur, departs 8:00 a.m., arrives 11:00 a.m. (3 h). At what time do the two trains meet?

Introduction / Context:
Assume constant speeds on the same route. Let the one-way distance be D. Speed of Train M = D/4 (h^−1), speed of Train D = D/3 (h^−1). The second train starts later, so first compute distance Train M covers by 8:00 a.m., then use relative speed to find the meeting time after 8:00 a.m.

Given Data / Assumptions:

• Train M speed = D/4 per hour.
• Train D speed = D/3 per hour.
• By 8:00 a.m., Train M has run 2 h ⇒ distance = D/2.

Concept / Approach:
Remaining separation at 8:00 a.m. = D − D/2 = D/2. After 8:00 a.m., closing speed = D/4 + D/3 = 7D/12 per hour. Time after 8:00 a.m. to meet = (D/2) / (7D/12) = 6/7 h ≈ 0 h 51 m 26 s.

Step-by-Step Solution:

Verification / Alternative check:
Distances after 8:00 a.m.: M covers (D/4)*(6/7) = 3D/14; D covers (D/3)*(6/7) = 2D/7; sum = 3D/14 + 2D/7 = D/2, consistent.

Why Other Options Are Wrong:
7:56 a.m. is too early (before Train D departs). 8:56 a.m. is several minutes late. p.m. options are irrelevant.

Common Pitfalls:
Taking an average of clock times or ignoring the 2 h head start.

Final Answer:
None of these (correct ≈ 8:51 a.m.)