A fast moving superfast express train crosses a slower passenger train in 20 seconds. The speed of the faster train is 72 km/h and the speed of the slower train is 27 km/h. The length of the faster train is 100 metres. If both trains are moving in the same direction on parallel tracks, what is the length (in metres) of the slower train?

Introduction / Context:
This question is a standard relative speed and trains problem. When one train overtakes another, the time taken depends on their relative speed and the total distance that must be covered, which is the sum of their lengths. We are given the speeds, the time of overtaking, and the length of the faster train, and must determine the length of the slower train.

Given Data / Assumptions:

• Speed of the faster train = 72 km/h.
• Speed of the slower train = 27 km/h.
• Length of the faster train = 100 metres.
• Time taken to completely cross the slower train = 20 seconds.
• Both trains move in the same direction on parallel tracks.

Concept / Approach:
When two bodies move in the same direction, their relative speed is the difference of their speeds. During overtaking, the faster train has to cover a distance equal to the sum of the lengths of both trains with respect to the slower train. We convert the speeds from km/h to m/s, compute the relative speed, multiply by time to get the total distance covered, and then subtract the known length of the faster train to obtain the length of the slower train.

Step-by-Step Solution:
Convert speeds to m/s using 1 km/h = 5/18 m/s. Speed of faster train = 72 × 5/18 = 20 m/s. Speed of slower train = 27 × 5/18 = 7.5 m/s. Relative speed when moving in the same direction = 20 - 7.5 = 12.5 m/s. Time taken to overtake = 20 seconds. Total distance covered relative to the slower train = relative speed × time = 12.5 × 20 = 250 metres. This total distance equals the sum of the lengths of both trains. Let L be the length of the slower train. Then 100 + L = 250. So L = 250 - 100 = 150 metres.

Verification / Alternative check:
We can verify by reversing the reasoning. If the slower train is 150 metres long, then combined length = 100 + 150 = 250 metres. At a relative speed of 12.5 m/s, time to cross is distance / speed = 250 / 12.5 = 20 seconds, matching the given value. So the answer is consistent.

Why Other Options Are Wrong:
100 m: Would imply combined length 200 metres, giving time = 200 / 12.5 = 16 seconds, not 20 seconds.
125 m and 175 m: These lengths would produce combined distances of 225 or 275 metres, which lead to overtaking times of 18 seconds or 22 seconds, neither matching the given 20 seconds.

Common Pitfalls:
Common mistakes include adding speeds instead of subtracting them for same-direction motion, forgetting to convert km/h to m/s, or mistakenly treating the distance to be covered as only one train length instead of the sum of both lengths. Always identify whether trains move in the same or opposite directions and convert units before applying formulas.

Final Answer:
The length of the slower passenger train is 150 metres.