यदि आपके पास दो सीधी 7·5 फुट और 3·25 फुट की छड़ें हैं, तो आप कम-से-कम कितनी लम्बाई नाप सकते हैं?
Read this question in English
If you have two straight sticks of length 7.5 feet and 3.25 feet, what is the minimum length can you measure?
(a) 0.05 foot · (b) 0.25 foot · (c) 1 foot · (d) 3.25 feet
उत्तर और व्याख्या · explanation in English
Answer: (b) 0·25 फुट
Laying the sticks end to end, forwards or backwards, measures any whole-number combination of 7·5 and 3·25 feet. The smallest positive length such combinations can give is their HCF, 0·25 foot.
- Convert to hundredths of a foot: 7·5 = 750/100 and 3·25 = 325/100.
- HCF(750, 325) = 25 (750 = 2 × 3 × 5³ and 325 = 5² × 13), so HCF of the lengths = 0·25 foot.
- Any length made by laying the sticks forwards and backwards is a multiple of 0·25 foot, and 0·25 itself can be made.
- Check: 7 × 3·25 = 22·75 and 3 × 7·5 = 22·5; 22·75 − 22·5 = 0·25 foot.
Remember · The smallest length measurable with two rods (by adding and subtracting whole lengths) is the HCF of their lengths.
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). ·