There are two chemicals which do not react with each other. A container contains 10 litres of the chemical A. One litre of this chemical is removed from it and one litre of the chemical B is poured. Then one litre of the mixture is removed from the container and one litre of B is poured. If this process of replacing one litre of the mixture by one litre of B is performed once more, then what is the volume of B that is present in the container approximately (in percentage)?
- (a) 25
- (b) 27 ✓ UPSC's answer
- (c) 29
- (d) 31
Why the answer is (b)
• Each replacement removes 1/10 of the mixture, so the amount of A left is multiplied by 9/10 each time.
• A is replaced three times in all: A left = 10 × (9/10)³ = 7·29 litres.
• B = 10 − 7·29 = 2·71 litres, i.e. about 27% of the 10 litres: (b).
Why the other options are wrong
- (a) 25
- 25% would need less B than three replacements give.
- (c) 29
- 29% is too high; after three replacements B is 2·71 litres.
- (d) 31
- 31% is too high; after three replacements B is 2·71 litres.
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.