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)
• Initially, the container holds 10 litres of Chemical A and 0 litres of Chemical B.
• After the first replacement, 1 litre of A is removed and 1 litre of B is added, leaving 9 litres of A and 1 litre of B.
• The concentration of A in the mixture is now 9/10 or 0.9.
• In the second step, 1 litre of the mixture is removed, which contains 0.9 litres of A, leaving 8.1 litres of A in the container.
• After adding 1 litre of B, the total volume of A is 8.1 litres out of 10 litres, meaning the volume of B is 10 - 8.1 = 1.9 litres.
• In the third step, 1 litre of the mixture is removed, containing 0.81 litres of A (since 8.1/10 = 0.81), leaving 8.1 - 0.81 = 7.29 litres of A.
• The final volume of B is 10 - 7.29 = 2.71 litres, which is 27.1% of the total volume, approximately 27%.
Why the other options are wrong
- (a) 25
- 25% would imply 2.5 litres of B, which corresponds to a different number of steps or incorrect dilution calculation.
- (c) 29
- 29% would imply 2.9 litres of B, which is higher than the calculated 2.71 litres.
- (d) 31
- 31% would imply 3.1 litres of B, which is significantly higher than the calculated 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.