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?
Answer & explanation
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). ·