A train covers a distance of 10 km in 12 minutes. If its speed is decreased by 5 km/hr, the time taken by it to cover the same distance will be

### Concept & Speed Calculation First determine the initial speed using the given distance and time, apply the speed reduction, and then calculate the new time for the same distance. $$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$ ### Step-by-Step Solution * Distance = 10 km, Initial Time = 12 minutes = $\frac{12}{60}$ hours = $\frac{1}{5}$ hours. * Initial Speed = $\frac{10}{\frac{1}{5}} = 50$ km/hr. * New Speed = $50 - 5 = 45$ km/hr. * New Time = $\frac{\text{Distance}}{\text{New Speed}} = \frac{10}{45}$ hours = $\frac{2}{9}$ hours. * Convert to minutes: $\frac{2}{9} \times 60 = \frac{120}{9} = \frac{40}{3}$ minutes = $13\frac{1}{3}$ minutes. * Convert $\frac{1}{3}$ minute to seconds: $\frac{1}{3} \times 60 = 20$ seconds. Total time = 13 min 20 sec. ### Exam Strategy & Shortcut Original speed is $10 \times 5 = 50$ (since 12 mins is $1/5$ hr). Decreased speed is 45. The ratio of new speed to old speed is $45/50 = 9/10$. Time is inversely proportional, so the new time is $10/9$ of the old time. $\frac{10}{9} \times 12 = \frac{120}{9} = \frac{40}{3}$ mins = 13 mins 20 secs. ### Common Pitfall Subtracting the 5 km/hr directly from the minutes or forgetting to convert the initial 12 minutes into hours before calculating the speed in km/hr. ### Final Answer Therefore, the correct answer is **13 min 20 sec**.