एक कार v km/hr की औसत चाल से स्थान X से स्थान Y तक यात्रा करती है, Y से X तक 2v km/hr की औसत चाल से, फिर X से Y तक 3v km/hr की औसत चाल से और फिर Y से X तक 4v km/hr की औसत चाल से यात्रा करती है। तो संपूर्ण यात्रा के लिए कार की औसत चाल
Read this question in English
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
(a) is less than v km/hr · (b) lies between v and 2v km/hr · (c) lies between 2v and 3v km/hr · (d) lies between 3v and 4v km/hr
उत्तर और व्याख्या · explanation in English
Answer: (b) v और 2v km/hr के बीच रहती है
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). ·