Along a straight railway track, a jogger runs at 9 km/h and is 240 m ahead of the engine of a train 120 m long that is moving at 45 km/h in the same direction. After how many seconds will the train completely pass the jogger?

Introduction / Context:
This aptitude question on trains and joggers tests the core concept of relative speed and the extra distance that a train has to travel in order to completely pass a moving person. Such questions are very common in competitive exams because they combine unit conversion, distance–time relations, and careful reading of the phrase "completely pass". Understanding how to model the situation in terms of relative motion is essential for solving similar questions quickly and accurately.

Given Data / Assumptions:

• Speed of the jogger = 9 km/h, moving along the track.
• Speed of the train = 45 km/h in the same direction.
• Initial distance between the jogger and the engine of the train = 240 m.
• Length of the train = 120 m.
• We assume both jogger and train maintain constant speeds and move in a straight line.

Concept / Approach:
The main idea is relative speed between two bodies moving in the same direction. When both move in the same direction, the effective speed at which one closes the gap on the other is the difference of their speeds. To completely pass the jogger, the front of the train must first cover the initial gap and then the full length of the train must go past the jogger. Total distance to be covered at relative speed is therefore initial gap plus train length.

Step-by-Step Solution:
Relative speed in km/h = 45 − 9 = 36 km/h. Convert 36 km/h to m/s: 36 * (5 / 18) = 10 m/s. Initial gap between train engine and jogger = 240 m. Train length = 120 m. Total distance that the train front must cover to completely pass the jogger = 240 m + 120 m = 360 m. Time = distance / relative speed = 360 / 10 = 36 seconds.

Verification / Alternative check:
We can do a quick check by imagining the frame of reference of the jogger. In that frame, the jogger is at rest and the train approaches at 10 m/s. If the total length that must pass is 360 m, then a time of 36 seconds is reasonable because 10 m/s for 36 seconds covers exactly 360 m. The numbers are consistent and unit conversions are correct.

Why Other Options Are Wrong:
18 sec is too small because at 10 m/s the train would only cover 180 m, which is less than the required 360 m. 48 sec is too large and corresponds to a much bigger distance than needed. 72 sec is clearly far too long and would imply a much slower relative speed or a much longer total distance than actually given in the problem.

Common Pitfalls:
Many learners forget to add both the initial gap and the train length, and instead use only the gap or only the length. Another common mistake is to add the speeds instead of subtracting them when bodies move in the same direction. Some students also forget to convert km/h to m/s correctly, which leads to numerical errors even when the method is right.

Final Answer:
Thus, the train will completely pass the jogger in 36 sec.