Q. A train completes a journey with a few stoppages in between at an average speed of 40 km per hour. If the train had not stopped anywhere, it would have completed the journey at an average speed of 60 km per hour. On average, how many minutes per hour does the train stop during the journey? (UPSC Prelims 2007)
Answer: 20 minutes per hour
Notes: Let the distance be D km. Actual time including stops is T₁ = D/40 hours, while non-stop time is T₂ = D/60 hours. The stoppage time per journey is Tₛ = T₁ - T₂ = D(1/40 - 1/60) = D/120 hours. The fraction of stoppage time to total time is (D/120) ÷ (D/40) = 1/3, meaning the train stops one-third of an hour per hour, equal to 20 minutes per hour. This calculation uses the average speed formula: Average speed = Total distance ÷ Total time.