A train of length 200 metres is moving at a speed of 72 km/h. How much time (in seconds) will it take to completely cross another train of length 300 metres that is moving in the same direction at 36 km/h?

Introduction / Context:
This question deals with two trains moving in the same direction at different speeds. To find the crossing time, we need to consider their relative speed and the total distance that must be covered for one train to pass the other completely. This type of train problem is a classic example of using relative motion in aptitude tests.

Given Data / Assumptions:

• Length of the first train = 200 m.
• Speed of the first train = 72 km/h.
• Length of the second train = 300 m.
• Speed of the second train = 36 km/h.
• Both trains move in the same direction.
• Speeds are constant and motion is in a straight line.

Concept / Approach:
When two objects move in the same direction, the effective speed at which one overtakes the other is the difference in their speeds. For one train to completely cross the other, it must cover a distance equal to the sum of both train lengths. We first compute the relative speed in m/s and then use time = distance / speed to find the crossing time in seconds.

Step-by-Step Solution:
Step 1: Convert speeds from km/h to m/s. Step 2: 72 km/h = 72 * 5/18 = 20 m/s. Step 3: 36 km/h = 36 * 5/18 = 10 m/s. Step 4: Relative speed when moving in the same direction = 20 - 10 = 10 m/s. Step 5: Total distance to be covered = 200 + 300 = 500 m. Step 6: Time to cross = distance / relative speed = 500 / 10 = 50 seconds.

Verification / Alternative check:
We can confirm by reversing roles. Regardless of which train is considered as overtaking, the relative speed remains 10 m/s and the total distance is 500 m. Hence the crossing time is always 500 / 10 = 50 seconds. This symmetry confirms the robustness of the calculation.

Why Other Options Are Wrong:
Times like 58, 60, or 62 seconds correspond to smaller relative speeds or larger distances than given, which do not reflect the actual numerical values. The distractor 55 seconds is close but still does not match the exact computation of 500 / 10 = 50, so it is also incorrect.

Common Pitfalls:
Learners sometimes add the speeds instead of subtracting them for same direction motion, which would be correct only for opposite directions. Forgetting to add both train lengths or mixing units between km/h and m/s are also frequent mistakes. Careful stepwise calculation avoids these issues.

Final Answer:
The train will take 50 sec to cross the other train completely.