The length of a bridge which a train 130 metres long, travelling at 45 km/h, can completely cross in 30 seconds is equal to how many metres?

Introduction / Context:
This question is about a train crossing a bridge, a classic type of quantitative aptitude problem. For the train to completely cross the bridge, the total distance it travels from the moment its front reaches the start of the bridge until its rear leaves the far end equals the sum of the train length and the bridge length. We know the train speed, the train length, and the time taken, so we can compute the bridge length.

Given Data / Assumptions:

• Length of the train = 130 m.
• Speed of the train = 45 km/h.
• Time taken to completely cross the bridge = 30 s.
• Speed is uniform and the track is straight.
• Total distance covered in 30 s = train length + bridge length.

Concept / Approach:
We first convert the speed from km/h to m/s to work consistently with metres and seconds. Then we use the formula distance = speed * time to find how far the train moves in 30 seconds. The bridge length is the excess of this total distance over the known train length. This method directly applies the idea that the train must clear its own length plus the bridge length.

Step-by-Step Solution:
Step 1: Convert 45 km/h to m/s using 1 km/h = 5/18 m/s. Step 2: 45 km/h = 45 * 5/18 = 225/18 = 12.5 m/s. Step 3: Total distance covered in 30 s = speed * time = 12.5 * 30 = 375 m. Step 4: This total distance equals train length + bridge length. Step 5: Bridge length = total distance - train length = 375 - 130 = 245 m. Step 6: Therefore, the bridge is 245 metres long.

Verification / Alternative check:
Check by reversing the calculation. If the bridge is 245 m and the train is 130 m, then total distance is 375 m. At 12.5 m/s, time needed = 375 / 12.5 = 30 s, which matches the given time. This confirms that our bridge length is consistent with the problem statement.

Why Other Options Are Wrong:
Bridge lengths such as 196, 210, 220, or 230 m would all lead to total distances less than 375 m, which, at 12.5 m/s, would result in times less than 30 seconds. Since the question explicitly states a crossing time of 30 seconds, these values cannot be correct.

Common Pitfalls:
Learners sometimes forget to add the train length when computing the distance needed to cross a bridge, using only the bridge length instead. Others may incorrectly convert 45 km/h to m/s or miscalculate the product of speed and time. Following the formula carefully with correct unit conversions avoids these errors.

Final Answer:
The length of the bridge is 245 m.