A train 100 m in length passes a milestone (point) in 10 s and another train of the same length coming from the opposite direction in 8 s. Find the speed of the second train (in km/h).

Introduction / Context:This problem combines a point-crossing time to determine the first train’s speed and a full-train crossing time (opposite directions) to determine relative speed, from which the second train’s speed follows by subtraction.

Given Data / Assumptions:

• Each train length = 100 m.
• First train passes a point in 10 s ⇒ speed1 = 100/10 = 10 m/s.
• Opposite-direction cross time for both trains together = 8 s.

Concept / Approach:For opposite directions, relative speed = (sum of individual speeds). To fully cross, required distance = sum of lengths = 200 m. Hence v_rel = 200/8 = 25 m/s. Therefore speed2 = v_rel − speed1.

Step-by-Step Solution:

Verification / Alternative check:Check: 36 + 54 = 90 km/h; in m/s that is 25 m/s; 200/25 = 8 s, consistent.

Why Other Options Are Wrong:36 km/h is the first train; 48 and 60 km/h lead to wrong crossing times.

Common Pitfalls:Forgetting to add lengths for full crossing or mixing up km/h and m/s conversions.

Final Answer:54 kmph