A train 110 m long is running at a speed of 72 km/h. How much time (in seconds) will it take to completely cross a bridge of length 132 m?

Introduction / Context:
This question involves a train passing over a bridge and asks for the time taken. It uses the standard idea that when a train crosses a bridge, the distance travelled is the sum of the train length and the bridge length, and that we must convert the speed to compatible units before applying the time formula.

Given Data / Assumptions:

• Train length = 110 m.
• Bridge length = 132 m.
• Speed of train = 72 km/h.
• Train moves at constant speed throughout the crossing.

Concept / Approach:
We first compute the total distance the train must travel while fully crossing the bridge, which is train length plus bridge length. Then we convert the speed from km/h to m/s so that distance in metres divided by speed in metres per second gives time in seconds. This is a direct application of time = distance / speed.

Step-by-Step Solution:
Step 1: Total distance to be covered while crossing the bridge = 110 + 132 = 242 m. Step 2: Convert speed 72 km/h to m/s using 1 km/h = 5/18 m/s. Step 3: Speed in m/s = 72 * 5 / 18 = 20 m/s. Step 4: Use time = distance / speed, so time = 242 / 20 seconds. Step 5: Compute 242 / 20 = 12.1 seconds.

Verification / Alternative check:
Check by approximate reasoning. At 20 m/s, in 10 seconds the train covers 200 m, and in 2.1 seconds it covers about 42 m, giving a total of 242 m in 12.1 seconds. This matches the distance we calculated and fits the given values. Therefore the computed time is consistent and correct.

Why Other Options Are Wrong:

• 9.8 sec: This is too short. At 20 m/s, the train would cover only 196 m in this time, less than 242 m.
• 12.42 sec and 14.3 sec: These are larger than the correct time. At these durations, the train would cover more than 242 m, which contradicts the requirement.

Common Pitfalls:
Typical mistakes include using only the train length instead of train plus bridge length, or forgetting to convert the speed properly from km/h to m/s. Some learners also misplace decimals when dividing the total distance by the speed, so it is important to compute carefully or simplify fractions before performing the division.

Final Answer:
The train will take 12.1 sec to cross the bridge completely.