A train 170 m long is running at 63 km/h. It can completely cross a bridge in 30 seconds. What is the length of the bridge in metres?

Introduction / Context:
This question checks understanding of how to calculate distance travelled by a moving train in a given time and how that distance relates to the lengths of both the train and the bridge it crosses. Problems of this type are standard in quantitative aptitude tests, and mastering them helps in quickly solving a variety of train and motion questions.

Given Data / Assumptions:

• Length of the train = 170 m.
• Speed of the train = 63 km/h.
• Time taken to completely cross the bridge = 30 seconds.
• The train runs at constant speed and the bridge is straight.
• When the train has completely crossed the bridge, its entire length has moved beyond the far end of the bridge.

Concept / Approach:
When a train crosses a bridge, the distance it travels from the moment its front enters the bridge until its rear leaves the bridge is equal to train length plus bridge length. Using speed and time, we find the total distance covered and then subtract the known train length to get the bridge length. Unit conversion from km/h to m/s is necessary to match with seconds and metres.

Step-by-Step Solution:
Speed in m/s = 63 * (5 / 18) = 17.5 m/s. Time taken to cross the bridge = 30 s. Total distance covered in this time = speed * time = 17.5 * 30 = 525 m. This total distance equals train length + bridge length. Bridge length = 525 m − 170 m = 355 m.

Verification / Alternative check:
We can check the calculation by reversing it. If the bridge is 355 m long, total effective length to clear is 170 m + 355 m = 525 m. At 17.5 m/s, time needed is 525 / 17.5 = 30 s, which matches the given information. This confirms that the result is consistent and accurate.

Why Other Options Are Wrong:
325 m would give a total distance of 495 m, leading to a time less than 30 s. 312 m yields a total of 482 m, which also contradicts the 30 s duration. 365 m gives a total of 535 m, leading to more than 30 s. None of these match the correct combination of speed and time given in the question.

Common Pitfalls:
A very common error is to forget that the train must travel its own length plus the bridge length, not only the length of the bridge. Another mistake is to mix units and multiply km/h directly by seconds without converting to m/s, which produces incorrect numerical values. Careful attention to units and the physical meaning of “completely cross” avoids these issues.

Final Answer:
Therefore, the length of the bridge is 355 m.