A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

### Concept & Logic When a train crosses a stationary man (a point object), the distance covered is exactly its own length. When it crosses a platform, the distance covered is its length plus the platform's length. $$ \text{Distance} = \text{Speed} \times \text{Time} $$ ### Step-by-Step Solution * **Given:** * Speed of train = $54$ km/hr = $54 \times \frac{5}{18} = 15$ m/s. * Time to cross man = $20$ seconds. * Time to cross platform = $36$ seconds. * **Calculation:** * The length of the train is the distance covered while crossing the man: $15 \text{ m/s} \times 20 \text{ s} = 300$ m. * The total distance covered while crossing the platform: $15 \text{ m/s} \times 36 \text{ s} = 540$ m. * Length of the platform = Total distance - Length of train. * Length of platform = $540 - 300 = 240$ m. ### Exam Strategy & Shortcut Since the train crosses its own length in $20$ seconds, it uses the remaining $16$ seconds ($36 - 20$) purely to cover the length of the platform. Length of platform = $15 \text{ m/s} \times 16 \text{ s} = 240$ m. ### Common Pitfall A common mistake is multiplying the speed directly by the total time ($36$ seconds) and assuming the result ($540$ m) is the length of the platform, neglecting to subtract the train's length. ### Final Answer Therefore, the correct answer is **240 m**.