A train takes 9 sec to cross a pole: If the speed of the train is 48 kmph, then length of the train is [Indian Railway Group 'D' Exam, 2014]

### Concept & Formula When a train crosses a pole (a point object), the distance covered is equal to the length of the train itself. Convert speed from kmph to m/s by multiplying by $\frac{5}{18}$. $$ \text{Length} = \text{Speed} \times \text{Time} $$ ### Step-by-Step Solution 1. **Convert Speed:** - Speed = $48$ kmph = $48 \times \frac{5}{18} = \frac{240}{18} = \frac{40}{3}$ m/s. 2. **Calculate Length:** - Time = 9 seconds. - Length = $\frac{40}{3} \times 9 = 40 \times 3 = 120$ m. ### Exam Strategy & Shortcut Simplify fractions early. Notice that $48 \times \frac{5}{18}$ simplifies by dividing by 6 ($\frac{8 \times 5}{3} = \frac{40}{3}$), which then easily multiplies with 9 to give $40 \times 3 = 120$. ### Common Pitfall Forgetting to convert kmph to m/s, which results in multiplying 48 by 9 directly and getting completely incorrect magnitudes. ### Final Answer Therefore, the correct answer is **120 m**.