Trains A and B start simultaneously from stations X and Y towards each other. After meeting, A takes 4 h 48 min to reach Y and B takes 3 h 20 min to reach X. If A's speed is 45 km/h, find the speed of B.

Introduction / Context:
For two trains starting from opposite ends and meeting once, the distances remaining after the meeting are proportional to their speeds, hence the times to finish are inversely proportional to their speeds. This yields a simple ratio to relate speeds using the post-meeting times.

Given Data / Assumptions:

• Time after meeting: t_A = 4 h 48 min = 4.8 h; t_B = 3 h 20 min = 3.333... h.
• Speed of A: v_A = 45 km/h.
• Straight track, constant speeds.

Concept / Approach:
Speeds are inversely proportional to the post-meeting times: v_A / v_B = t_B / t_A. Solve for v_B, then check consistency.

Step-by-Step Solution:

Verification / Alternative check:
v_A : v_B = 45 : 64.8 = 25 : 36, matching t_B : t_A = 25 : 36 inverted.

Why Other Options Are Wrong:
60 km/h and 54 km/h do not satisfy the inverse-time ratio; 37.5 km/h would make B slower than A, contradicting the times.

Common Pitfalls:
Using direct (not inverse) proportionality or mis-converting minutes to hours.

Final Answer:
64.8 km/hr