Two trains of equal length are running in opposite directions at the same uniform speed. The length of each train is 120 metres. If they completely cross each other in 12 seconds, what is the speed of each train in km/h?

Introduction / Context:
This question is a classic trains problem involving relative speed when two trains move in opposite directions. It checks whether a student can correctly apply the idea that when bodies move towards each other, their relative speed is the sum of their individual speeds, and then convert from metres per second to kilometres per hour.

Given Data / Assumptions:

• Each train is 120 metres long.
• The trains are moving in opposite directions with the same speed.
• They completely cross each other in 12 seconds.
• The motion is along the same straight track, and speeds are constant.
• We must find the speed of each train in km/h.

Concept / Approach:
When two trains move in opposite directions, the distance to be covered when they cross each other is the sum of their lengths. Since both lengths are equal here, the total crossing distance is 120 + 120 metres. The relative speed when moving in opposite directions is the sum of their individual speeds. Once the relative speed in metres per second is found from distance divided by time, we divide by 2 to get the speed of each train, and finally convert this speed into km/h using the standard factor 18 / 5.

Step-by-Step Solution:
Step 1: Total length to be covered while crossing each other = 120 + 120 = 240 metres.Step 2: Time taken to cross each other = 12 seconds, so relative speed = 240 / 12 = 20 metres per second.Step 3: Since the trains have equal speed and move in opposite directions, each train has speed = relative speed / 2 = 20 / 2 = 10 metres per second.Step 4: Convert this speed into km/h using 1 metre per second = 18 / 5 km/h.Step 5: Speed in km/h = 10 * 18 / 5 = 10 * 3.6 = 36 km/h.

Verification / Alternative check:
If each train runs at 36 km/h, then in metres per second the speed is 36 * 5 / 18 = 10 metres per second.Relative speed in opposite directions = 10 + 10 = 20 metres per second.Time = distance / speed = 240 / 20 = 12 seconds, which matches the given crossing time.

Why Other Options Are Wrong:
20 km/h and 28 km/h are too low; if each train had such a speed, the time required to cross would be higher than 12 seconds. The option 42 km/h is higher than the correct value and would lead to a shorter crossing time. The option 32 km/h does not satisfy the exact condition when checked back using distance and time.

Common Pitfalls:
Many learners forget to add the lengths of both trains when they cross each other and instead use only one length. Another common mistake is to forget that the speeds add when trains move in opposite directions. Finally, some students perform the km/h to m/s conversion incorrectly, using 5 / 18 instead of 18 / 5 or vice versa in the wrong place. Careful unit handling avoids such errors.

Final Answer:
Each train is moving at a speed of 36 km/h.