A train 125 m long passes a man who is running at 5 km/h in the same direction as the train in 10 seconds. What is the speed of the train in km/h?

Introduction / Context:
This question tests relative speed concepts when a train overtakes a man moving in the same direction. The train length and overtaking time are given, and the objective is to find the speed of the train in km/h. Such questions are common in aptitude exams and help develop quick reasoning about motion along a straight line.

Given Data / Assumptions:

• Length of the train = 125 m.
• Speed of the man = 5 km/h.
• Time taken by the train to pass the man completely = 10 s.
• The man and the train move in the same direction.
• Speeds are constant and motion is along a straight track.

Concept / Approach:
The train has to cover its own length relative to the man in order to overtake him fully. Therefore, the relevant speed is the relative speed between the train and the man, which is the difference between their speeds in the same direction. We can first compute the relative speed in m/s using distance and time, then convert that into km/h and finally add the man's speed to get the train's speed.

Step-by-Step Solution:
Relative distance to be covered = length of train = 125 m. Time to overtake = 10 s. Relative speed in m/s = distance / time = 125 / 10 = 12.5 m/s. Convert relative speed to km/h: 12.5 * (18 / 5) = 12.5 * 3.6 = 45 km/h. Let speed of train = V km/h. Then relative speed = V − 5. So, V − 5 = 45 which gives V = 50 km/h.

Verification / Alternative check:
Check by forward calculation: If the train moves at 50 km/h and the man at 5 km/h, relative speed = 45 km/h. In m/s, this is 45 * 5 / 18 = 12.5 m/s. Time to cover the train length 125 m = 125 / 12.5 = 10 s, which agrees with the given time.

Why Other Options Are Wrong:
If the train speed were 45 km/h, relative speed would be only 40 km/h, leading to a different overtaking time. Similarly, speeds 25 km/h or 30 km/h are much too slow and cannot allow the train to pass a man moving at 5 km/h in 10 seconds. Only 50 km/h satisfies both the relative speed and time conditions.

Common Pitfalls:
Some learners mistakenly add the speeds instead of subtracting them in same direction motion. Others compute relative speed correctly but forget to add the man's speed back to obtain the train's speed. Careful interpretation of the phrase "same direction" and a two step approach for relative and actual speeds help avoid these mistakes.

Final Answer:
The speed of the train is 50 km/h.