Train P leaves Mokama at 5:00 pm and reaches Hazipur at 6:00 pm (1 hour). Train Q leaves Hazipur at 5:00 pm and reaches Mokama at 6:30 pm (1.5 hours). Assuming constant speeds and simultaneous start at 5:00 pm, at what time do they meet?

Introduction / Context:
Two trains start simultaneously from opposite stations and move towards each other with constant speeds. The ratio of their speeds equals the inverse ratio of their individual travel times over the same fixed distance. Meeting time is obtained from the sum of distances covered until meeting equaling the full inter-station distance.

Given Data / Assumptions:

• P takes 1 h for the full route ⇒ v_P = D / 1 h.
• Q takes 1.5 h ⇒ v_Q = D / 1.5 h.
• They start at 5:00 pm from opposite stations and move towards each other.

Concept / Approach:
At meeting, v_P * t + v_Q * t = D. Express each speed as a fraction of D per hour; solve for t in hours, then convert to minutes to get the wall-clock time after 5:00 pm.

Step-by-Step Solution:

Verification / Alternative check:
In 36 minutes, P covers 0.6D and Q covers 0.4D; together they span D.

Why Other Options Are Wrong:
Other times do not correspond to t = 36 minutes after a simultaneous 5:00 pm start.

Common Pitfalls:
Mistaking absolute times for durations; always compute elapsed time from the simultaneous start.

Final Answer:
5 : 36 pm