A train 240 m long passed a pole in 24 seconds. How long will it take to pass a platform 650 m long?

### Concept & Formula When a train crosses a stationary pole, the distance covered is equal to its own length. This helps us find its speed. When crossing a platform, the total distance covered is the sum of the train's length and the platform's length. $$ \text{Speed} = \frac{\text{Length of Train}}{\text{Time to cross pole}} $$ $$ \text{Time to cross platform} = \frac{\text{Length of Train} + \text{Length of Platform}}{\text{Speed}} $$ ### Step-by-Step Solution * **Find Speed:** The train covers $240$ m in $24$ seconds to cross the pole. * Speed = $\frac{240}{24} = 10$ m/s. * **Find Total Distance:** To cross the platform, distance = $240$ m (train) + $650$ m (platform) = $890$ m. * **Calculate Time:** Time = $\frac{\text{Total Distance}}{\text{Speed}} = \frac{890}{10} = 89$ seconds. ### Exam Strategy & Shortcut Observe the proportionality. The train covers $240$ m in $24$ seconds, meaning it takes exactly $1$ second for every $10$ meters. To cover a total distance of $890$ meters ($240 + 650$), it will take $890 / 10 = 89$ seconds. ### Common Pitfall Calculating the time for the platform alone ($650 / 10 = 65$ seconds) without accounting for the train's own length that must also clear the platform. ### Final Answer Therefore, the correct answer is **89 sec**.