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 ✓ UPSC's answer
- (c) 9
- (d) 10
Why the answer is (b)
• Let the number of 1 kg weights be a (8 to 11). The rest, 20 − a, must be made from 2, 5 and 10 kg weights.
• a = 8, rest 12: 6 × 2; 1 × 2 + 2 × 5; 1 × 2 + 1 × 10. Three ways.
• a = 9, rest 11: 3 × 2 + 1 × 5. One way.
• a = 10, rest 10: 5 × 2; 2 × 5; 1 × 10. Three ways. a = 11, rest 9: 2 × 2 + 1 × 5. One way.
• Total 3 + 1 + 3 + 1 = 8: (b).
Why the other options are wrong
- (a) 7
- 7 misses one of the eight combinations listed.
- (c) 9
- 9 counts a combination that does not total 20 kg.
- (d) 10
- 10 overcounts; only eight combinations are possible.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.