A car travels from a place X to place Y at an average speed of v km/hr, from Y to X at an average speed of 2v km/hr, again from X to Y at an average speed of 3v km/hr and again from Y to X at an average speed of 4v km/hr. Then the average speed of the car for the entire journey
Answer & explanation
Answer: (b) lies between v and 2v km/hr
All four legs cover the same distance, so the slow legs take the most time and pull the average down. Total time = (d/v)(1 + 1/2 + 1/3 + 1/4) = 25d/12v for a distance of 4d, giving an average of 48v/25 = 1·92v.
- Let XY = d km. Total distance = 4d.
- Total time = d/v + d/2v + d/3v + d/4v = (d/v)(12 + 6 + 4 + 3)/12 = 25d/12v.
- Average speed = 4d ÷ (25d/12v) = 48v/25 = 1·92v.
- 1·92v lies between v and 2v.
Remember · For equal distances at different speeds, average speed is the harmonic mean — always closer to the slower speeds.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·