A goods train runs at a speed of 72 km/h and crosses a platform that is 250 metres long in 26 seconds. What is the length of the goods train in metres?

Introduction / Context:
This is a straightforward train and platform question where the length of the train has to be found from its speed, the time taken to pass the platform, and the known platform length. It reinforces the relationship between speed, distance and time and proper unit conversion from km/h to metres per second.

Given Data / Assumptions:

• Speed of the goods train = 72 km/h.
• Length of the platform = 250 metres.
• Time taken to cross the platform completely = 26 seconds.
• The train moves at uniform speed.
• We must determine the length of the train.

Concept / Approach:
When a train passes a platform, the distance it travels from the instant its front end reaches the platform to the instant its rear end leaves the platform is equal to the sum of the train length and the platform length. We first convert the train's speed into metres per second, then multiply by the time to get the total distance travelled during crossing, and finally subtract the platform length to obtain the train length.

Step-by-Step Solution:
Step 1: Convert speed from km/h to metres per second: 72 km/h = 72 * 5 / 18 = 20 metres per second.Step 2: Total distance covered while crossing the platform = speed * time = 20 * 26 = 520 metres.Step 3: Let the train length be L metres. Then L + 250 = 520.Step 4: Solve for L: L = 520 - 250 = 270 metres.

Verification / Alternative check:
Using L = 270 metres, total distance while crossing platform = 270 + 250 = 520 metres.At 20 metres per second, time = 520 / 20 = 26 seconds, which exactly matches the given time.

Why Other Options Are Wrong:
Train lengths such as 230 metres, 240 metres, 260 metres or 280 metres do not result in a total distance of 520 metres when added to the platform length, and therefore do not produce the correct crossing time of 26 seconds at 72 km/h. When checked, each one either gives a time shorter or longer than 26 seconds.

Common Pitfalls:
Some students forget to convert speed from km/h into metres per second and directly multiply by time in seconds, which mixes inconsistent units. Others may mistakenly subtract the platform length first or confuse the formula, using distance minus platform instead of distance equals train length plus platform length. Keeping the interpretation of distance clear eliminates these issues.

Final Answer:
The length of the goods train is 270 metres.