Problems on Trains – Bridge length from crossing time: A 200 m long train runs at 36 km/h and crosses a bridge in 30 seconds. What is the length of the bridge?

Introduction / Context:
When a train crosses a bridge, the total distance traveled during the crossing equals train length + bridge length. With speed and total time known, compute the total crossing distance and subtract the train length to get the bridge length.

Given Data / Assumptions:

• L_train = 200 m.
• Speed = 36 km/h = 10 m/s.
• Crossing time = 30 s.

Concept / Approach:
Total distance = speed * time. Then L_bridge = total distance − L_train.

Step-by-Step Solution:
Speed = 36 * (1000/3600) = 10 m/s.Total distance = 10 * 30 = 300 m.Bridge length = 300 − 200 = 100 m.

Verification / Alternative check:
Check: At 10 m/s, 100 m are covered in 10 s. The remaining 200 m (train length) take 20 s. Sum = 30 s, consistent.

Why Other Options Are Wrong:
150 m, 200 m, 125 m, 180 m do not satisfy total distance = 300 m with the given train length.

Common Pitfalls:
Forgetting to convert speed to m/s or failing to add train and bridge distances when forming the total crossing distance.

Final Answer:
100 m