What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey?
- (a) 20% ✓ UPSC's answer
- (b) 10%
- (c) 5%
- (d) 4%
Why the answer is (a)
• Let the honey cost ₹1 per litre, and mix w litres of water with 1 litre of honey.
• Cost of the mixture = ₹1 (only the honey costs money). It is sold at the cost price of honey: (1 + w) litres × ₹1 = ₹(1 + w).
• A 20% gain needs 1 + w = 1.2, so w = 0.2 litre of water per litre of honey.
• The water mixed is 20% of the honey — option (a). (As a share of the whole mixture it would be 1/6 ≈ 16.7%, which is not an option; the question measures water against the honey.)
Why the other options are wrong
- (b) 10%
- Mixing 10% water (0.1 litre per litre of honey) sells 1.1 litres for the cost of 1 litre — a 10% gain, not 20%.
- (c) 5%
- Mixing 5% water gives only a 5% gain.
- (d) 4%
- Mixing 4% water gives only a 4% gain.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.