A uniformly moving train 480 m long takes 3 minutes to completely cross a platform. If the same train at the same speed takes 30 seconds to completely pass a pole, what is the length (in metres) of the platform?

Introduction / Context:
This question combines two standard train scenarios. The train crosses a platform in a given time and also crosses a pole in a shorter time. Using the second situation, we can compute the train speed. Then, from the first situation, we compute the total distance travelled over the platform and finally extract the platform length.

Given Data / Assumptions:

• Length of train = 480 m.
• Time to completely cross a platform = 3 minutes = 180 seconds.
• Time to completely cross a pole = 30 seconds.
• The train moves at uniform (constant) speed in both situations.
• Crossing a pole involves only the train length, while crossing a platform involves train length plus platform length.

Concept / Approach:
First, we find the speed of the train from the pole crossing data, because distance and time are simple there. Once we know the speed in metres per second, we multiply it by the time taken to cross the platform to get the total distance travelled. The total distance equals train length plus platform length. Subtracting the known train length gives the platform length.

Step-by-Step Solution:
Step 1: When crossing a pole, distance = train length = 480 m. Step 2: Time to cross pole = 30 seconds, so speed = distance / time = 480 / 30 m/s. Step 3: Compute speed = 16 m/s. Step 4: When crossing the platform, time = 3 minutes = 180 seconds. Step 5: Total distance covered in 180 seconds = speed * time = 16 * 180 = 2880 m. Step 6: Total distance = train length + platform length. Step 7: So 2880 = 480 + platform length. Step 8: Platform length = 2880 - 480 = 2400 m.

Verification / Alternative check:
We can check by recomputing times. With speed 16 m/s and platform length 2400 m, total distance when crossing platform is 480 + 2400 = 2880 m. Time = 2880 / 16 = 180 seconds, which is exactly 3 minutes. For the pole, distance is 480 m, time is 480 / 16 = 30 seconds, matching the given data. Both conditions are satisfied, so the platform length is correct.

Why Other Options Are Wrong:

• 600 m and 1200 m: These values would make the total distance too small and the time to cross platform much less than 3 minutes at the calculated speed.
• 4800 m: This would give a very large total distance 5280 m and time 5280 / 16 = 330 seconds, which is far greater than 3 minutes.

Common Pitfalls:
A typical mistake is to treat crossing a platform the same as crossing a pole and only consider train length. Another error is mixing seconds and minutes without proper conversion. Some learners incorrectly use the 3 minutes information first, which is more complex than using the simpler pole crossing to find speed. Always use the simplest case to find speed and then move to more complicated distances.

Final Answer:
The length of the platform is 2400 m.