A train 500 m long, running at a uniform speed, passes completely over a station platform 221 m long in 35 seconds. What is the speed of the train in km/hr?

Introduction / Context:
This trains and platforms question examines the idea that when a train passes completely over a platform, the effective distance covered during the crossing is the sum of the train's length and the platform's length. Using this total distance and the crossing time, we can calculate the speed of the train and then express it in km/hr.

Given Data / Assumptions:
- Length of the train = 500 m.
- Length of the platform = 221 m.
- Time taken to pass the station (platform) completely = 35 seconds.
- Train runs at a constant speed and there are no stops during the crossing.

Concept / Approach:
When a train crosses a platform, the distance it effectively travels, with respect to the platform, is the sum of its own length and the platform length. The basic relationship is speed = distance / time. We first compute the speed in m/s using total distance and time, and then convert this speed to km/hr by multiplying by 18 / 5.

Step-by-Step Solution:
Step 1: Total distance to be covered while crossing the platform = length of train + length of platform.Step 2: Total distance = 500 m + 221 m = 721 m.Step 3: Time taken = 35 seconds.Step 4: Speed in m/s = distance / time = 721 / 35 m/s.Step 5: Convert this speed to km/hr using the factor 18 / 5.Step 6: Speed in km/hr = (721 / 35) * (18 / 5) = (721 * 18) / 175.Step 7: Compute (721 * 18) = 12978, so speed = 12978 / 175 km/hr.Step 8: Divide 12978 by 175 to get 74.16 km/hr.

Verification / Alternative check:
As a quick check, note that 721 / 35 ≈ 20.6 m/s. Multiplying by 3.6 to convert to km/hr (which is equivalent to 18 / 5) gives 20.6 * 3.6 ≈ 74.16 km/hr. This matches the more detailed fraction-based calculation, confirming the correctness of the result.

Why Other Options Are Wrong:
72.1 km/hr and 68.4 km/hr are close but correspond to slightly different crossing times than 35 seconds when you recompute distance = speed * time. 24.76 km/hr is far too small for the given distance and time. 78.54 km/hr is a bit too high and would imply a shorter crossing time than 35 seconds. Only 74.16 km/hr matches the exact arithmetic.

Common Pitfalls:
One frequent mistake is to forget to include the platform length and use only the train length as the distance. Another is to convert the speed incorrectly, for example by using 5 / 18 instead of 18 / 5 when moving from m/s to km/hr. Some learners also round intermediate values prematurely, leading to slightly off answers instead of the exact 74.16 km/hr.

Final Answer:
The speed of the train is 74.16 km/hr.