चार प्रकार के बाट (weights) हैं, नामतः 1 kg, 2 kg, 5 kg और 10 kg. यदि मापते समय, कम-से-कम आठ, किन्तु ग्यारह से अनधिक 1 kg के बाटों का उपयोग किया जाना है, तो 20 kg के वज़न को अधिकतम कितने भिन्न प्रकार से मापा जा सकता है?
Read this question in English
There are four types of weights, namely 1 kg, 2 kg, 5 kg and 10 kg. What is the maximum number of different ways one can measure 20 kg, if at least eight but not more than eleven weights of 1 kg are to be used while measuring?
(a) 7 · (b) 8 · (c) 9 · (d) 10
उत्तर और व्याख्या · explanation in English
Answer: (b) 8
Fix the number of 1 kg weights at 8, 9, 10 or 11 and make up the rest with 2, 5 and 10 kg weights. The counts are 3, 1, 3 and 1, giving 8 ways.
- Eight 1 kg weights: 12 kg left → 10 + 2; 5 + 5 + 2; six 2s → 3 ways.
- Nine 1 kg weights: 11 kg left from 2, 5 and 10 kg weights. 11 is odd, so exactly one 5 is needed, plus three 2s → 1 way.
- Ten 1 kg weights: 10 kg left → 10; 5 + 5; five 2s → 3 ways.
- Eleven 1 kg weights: 9 kg left, odd again → 5 + 2 + 2 → 1 way.
- Total = 3 + 1 + 3 + 1 = 8.
Remember · Counting combinations of coins or weights: fix the most restricted item, then list the rest systematically from the largest.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·