A train 250 m long crosses a bridge 150 m long in 20 seconds. What is the speed of the train in km/h?

Introduction / Context:
This question tests understanding of how to compute speed when a train crosses a bridge. The key idea is that the train must cover its own length plus the length of the bridge. After obtaining the speed in metres per second, we convert it to kilometres per hour, which is a common conversion in aptitude questions on time and distance.

Given Data / Assumptions:

• Length of the train = 250 m.
• Length of the bridge = 150 m.
• Total time to cross the bridge completely = 20 seconds.
• Speed is assumed to be uniform.

Concept / Approach:
When a train crosses a bridge, the distance covered before it has completely cleared the bridge is equal to the sum of the length of the train and the length of the bridge. Then we use the formula speed = distance / time. Finally, we convert the result from m/s to km/h using the standard factor 18/5.

Step-by-Step Solution:
Total distance to be covered = length of train + length of bridge. Total distance = 250 m + 150 m = 400 m. Time taken = 20 s. Speed in m/s = distance / time = 400 / 20 = 20 m/s. To convert m/s to km/h, multiply by 18/5. Speed in km/h = 20 * (18 / 5) = 20 * 3.6 = 72 km/h.

Verification / Alternative check:
We can reverse check: at 72 km/h, speed in m/s is 72 * 5 / 18 = 20 m/s. In 20 seconds, distance covered = 20 * 20 = 400 m, which matches the sum of the train and bridge lengths. Therefore, the calculation is correct.

Why Other Options Are Wrong:

• 80 km/h: Gives speed in m/s as 80 * 5 / 18 which would cover more than 400 m in 20 s.
• 70 km/h: Corresponds to a slightly smaller speed and would lead to less than 400 m in 20 s.
• 92 km/h: Is far higher and clearly exceeds the required distance in the given time.

Common Pitfalls:
Many candidates forget to add both lengths and only use the train length, which underestimates the speed. Another frequent mistake is converting between m/s and km/h incorrectly, for example by multiplying with 5/18 instead of 18/5 when going from m/s to km/h.

Final Answer:
The speed of the train is 72 km/h.