A 150 m long train crosses a milestone in 15 seconds and a train of same length coming from the opposite direction in 12 seconds. The speed of the othe train is (R.R.B., 2006)

### Concept & Distance A train crossing a stationary object (like a milestone) covers a distance equal to its own length. When crossing another moving train, the distance is the sum of both lengths. $$ \text{Speed} = \frac{\text{Length}}{\text{Time}} $$ ### Step-by-Step Solution * Length of the first train = $150$ m. Time to cross milestone = 15 s. * Speed of the first train = $\frac{150}{15} = 10$ m/s. * Length of the second train = $150$ m (since it has the same length). * Total distance when crossing each other = $150 + 150 = 300$ m. * Time taken to cross each other = 12 s. * Relative speed = $\frac{300}{12} = 25$ m/s. * Since they move in opposite directions, Relative Speed = Speed 1 + Speed 2. * $10 + \text{Speed 2} = 25 \Rightarrow \text{Speed 2} = 15$ m/s. * Convert to kmph: $15 \times \frac{18}{5} = 54$ kmph. ### Exam Strategy & Shortcut You can calculate relative speed $25$ m/s and subtract the first train's speed ($10$ m/s) to get $15$ m/s. Multiply by $3.6$ for a rapid m/s to km/h conversion: $15 \times 3.6 = 54$ kmph. ### Common Pitfall Assuming the second train crosses a point in 12 seconds instead of crossing the first train. Always read whether it crosses a point or an object with length. ### Final Answer Therefore, the correct answer is **54 kmph**.