A train leaves Delhi at 4.10 P.M. and reaches Aligarh at 7.25 P.M. The average speed of the train is 40 km/hr. What is the distance from Delhi to Aligarh?

### Concept & Distance Formula The total distance covered is the product of the average speed and the total time taken for the journey. $$ \text{Distance} = \text{Speed} \times \text{Time} $$ ### Step-by-Step Solution * **Calculate Total Time:** The train starts at 4:10 P.M. and arrives at 7:25 P.M. * From 4:10 P.M. to 7:10 P.M. is exactly 3 hours. * From 7:10 P.M. to 7:25 P.M. is 15 minutes. * Total time = 3 hours 15 minutes. * Convert minutes to hours: 15 minutes = $\frac{15}{60}$ hours = $\frac{1}{4}$ hour. * Total time in hours = $3 + \frac{1}{4} = \frac{13}{4}$ hours. * **Calculate Distance:** Distance = $40 \text{ km/hr} \times \frac{13}{4} \text{ hr} = 10 \times 13 = 130 \text{ km}$. ### Exam Strategy & Shortcut Keep the time in a mixed fraction or improper fraction (like 13/4) rather than a decimal (3.25) to make cancellation with the speed (40) instantaneous. ### Common Pitfall Miscalculating the time difference. Students often incorrectly subtract the digital times (7.25 - 4.10 = 3.15) and treat the ".15" as a decimal fraction of an hour rather than minutes, leading to an incorrect multiplier of 3.15 instead of 3.25. ### Final Answer Therefore, the correct answer is **130 km**.