A passenger train is moving at a speed of 120 km/h. If the length of the train is 101 metres, how long (in seconds) will it take to completely cross a railway platform that is 154 metres long?

Introduction / Context:
This is a standard train and platform problem where the train must cover its own length plus the length of the platform in order to completely pass it. Such questions assess the ability to convert units, combine distances, and apply the basic relation speed = distance / time. Here, both the train length and the platform length are given, and we must compute the total time for the train to clear the platform.

Given Data / Assumptions:

• Speed of the train = 120 km/h.
• Length of the train = 101 m.
• Length of the platform = 154 m.
• The train moves at a uniform speed on straight track.
• To fully cross the platform, the train must travel a distance equal to train length plus platform length.

Concept / Approach:
First, the speed must be converted from km/h to m/s to match the distance units in metres. Next, the total distance to be covered while crossing the platform is the sum of the train length and platform length. Then we apply the formula time = distance / speed to find the required time, expressed in seconds.

Step-by-Step Solution:
Step 1: Convert speed from km/h to m/s. Step 2: 120 km/h = 120 * 5/18 m/s = 600/18 m/s = 33.333... m/s. Step 3: Calculate total distance = train length + platform length = 101 + 154 = 255 m. Step 4: Use time = distance / speed. Step 5: Time = 255 / 33.333... ≈ 7.65 seconds. Step 6: Therefore, the train takes approximately 7.65 seconds to cross the platform completely.

Verification / Alternative check:
We can verify by approximating the speed as 33.33 m/s. Then in 7.65 seconds, distance covered = 33.33 * 7.65 ≈ 255 metres, which equals the sum of the lengths of the train and the platform. This consistency check confirms that our time is correctly computed.

Why Other Options Are Wrong:
The values 6.24, 6.58, and 7.325 seconds would correspond to smaller distances at the same speed and hence would not allow the train to travel the full 255 metres. The distractor 8.25 seconds implies the train covers more distance than required, which does not match the exact condition that it should just clear the platform.

Common Pitfalls:
Students often forget to add the platform length to the train length, treating only the train length as the distance. Another frequent mistake is improper conversion between km/h and m/s, or rounding speed too early, which can cause noticeable errors in time. Carefully handling units and total distance prevents such errors.

Final Answer:
The train will take approximately 7.65 sec to cross the platform completely.