Two trains run on parallel lines in the same direction at 50 km/h (faster) and 30 km/h (slower). The faster train crosses a man sitting in the slower train in 18 s. Find the length of the faster train.

Introduction / Context:
When two objects move in the same direction, the relative speed is the difference of their speeds. The time to cross a point-object (a man) equals the length to be covered divided by the relative speed. Here, the “length to be covered” is the length of the faster train.

Given Data / Assumptions:

• Speeds: v_fast = 50 km/h, v_slow = 30 km/h.
• Time to cross the man: t = 18 s.
• Uniform speeds and straight tracks.

Concept / Approach:
Relative speed (same direction) v_rel = v_fast − v_slow. Convert km/h to m/s using 5/18. Length of faster train L = v_rel * t.

Step-by-Step Solution:

Verification / Alternative check:
At 100 m length and 50/9 m/s relative speed, time is 100 / (50/9) = 18 s, matching the given.

Why Other Options Are Wrong:
85 m, 98 m, 170 m give times different from 18 s at the computed relative speed.

Common Pitfalls:
Using sum of speeds instead of the difference for same-direction motion, or skipping unit conversion.

Final Answer:
100 metres