A train that is 200 m long is running at a uniform speed of 54 km/hr. How many seconds will it take for the entire train to completely cross a bridge that is 175 m long, from the moment the engine reaches the bridge until the last coach leaves it?

Introduction / Context:
This is a standard trains and relative motion question that focuses on the relationship between distance, speed, and time. The key idea is that when a train crosses a bridge or a platform, the distance it effectively covers is the sum of its own length and the length of the bridge. You then combine this distance with the speed (converted into consistent units) to find the time taken.

Given Data / Assumptions:
- Length of the train = 200 m.
- Length of the bridge = 175 m.
- Speed of the train = 54 km/hr (uniform speed).
- The train must completely cross the bridge, which means the whole 200 m must clear the bridge length.
- Motion is along a straight track with no acceleration or deceleration.

Concept / Approach:
The fundamental formula used in this problem is time = distance / speed. When a train crosses a bridge, the distance travelled from the instant the engine reaches the bridge until the last coach leaves it equals the sum of the train length and bridge length. Since the speed is given in km/hr and the lengths are in meters, we must convert the speed into meters per second before applying the formula. This ensures all units are consistent and avoids calculation mistakes.

Step-by-Step Solution:
Step 1: Total distance to be covered while crossing the bridge = length of train + length of bridge = 200 m + 175 m = 375 m.Step 2: Convert the train's speed from km/hr to m/s using the standard factor 5 / 18.Step 3: Speed in m/s = 54 * (5 / 18) = (54 / 18) * 5 = 3 * 5 = 15 m/s.Step 4: Use the time formula: time = distance / speed = 375 / 15 seconds.Step 5: Compute 375 / 15 = 25 seconds.Step 6: Therefore, the train takes exactly 25 seconds to completely cross the bridge.

Verification / Alternative check:
A quick reasonableness check: at 15 m/s, the train covers 150 m in 10 seconds, 300 m in 20 seconds, and 375 m in 25 seconds. This matches the calculated answer perfectly. Also, since both the train and bridge lengths are mid-range values and the speed is moderate, an answer around a few tens of seconds is realistic, which further supports 25 seconds as a sensible result.

Why Other Options Are Wrong:
20 seconds would correspond to a distance of 20 * 15 = 300 m, which is less than the 375 m required. 12.5 seconds would only allow the train to cover about 187.5 m. 18 seconds corresponds to 270 m, and 15 seconds corresponds to 225 m. None of these distances is enough to cover both the 200 m train and the 175 m bridge together.

Common Pitfalls:
Learners often forget to add the bridge length to the train length and mistakenly use only 200 m in the distance. Another frequent mistake is neglecting to convert 54 km/hr into m/s, which leads to inconsistent units and incorrect answers. Some also round the conversion unnecessarily, but using the exact factor 5 / 18 keeps the calculation clean and accurate.

Final Answer:
The train will take 25 seconds to completely cross the 175 m long bridge.