A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, then the length of the train is

### Concept & Formula First, find the speed of the train using the given distance and time. Once the uniform speed is known, use it along with the time taken to pass the pole to find the train's length. $$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$ $$ \text{Length of Train} = \text{Speed (m/s)} \times \text{Time to cross post (s)} $$ ### Step-by-Step Solution * **Given for Speed:** Distance = $12$ km = $12000$ m. Time = $10$ minutes = $10 \times 60 = 600$ seconds. * **Calculate Speed:** $\text{Speed} = \frac{12000}{600} = 20$ m/s. * **Given for Crossing:** Time to pass post = $6$ seconds. * **Calculate Length:** Length = $20 \text{ m/s} \times 6 \text{ s} = 120$ m. ### Exam Strategy & Shortcut $12$ km in $10$ minutes is equivalent to $72$ km in $60$ minutes ($72$ km/hr). We know $72$ km/hr is exactly $20$ m/s ($4 \times 18$ -> $4 \times 5$). Multiplying $20$ m/s by $6$ seconds immediately yields $120$ m. ### Common Pitfall Mixing units. If you use $12$ km and $10$ minutes directly, you might end up with speed in km/min and apply it incorrectly to the $6$ seconds. Always standardize to meters and seconds. ### Final Answer Therefore, the correct answer is **120 m**.