UPSC Prelims 2026 · CSAT
Question 79: Basic Numeracy
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)?
AnswerUPSC’s answer is (b).
Each replacement removes one tenth of whatever chemical A is present, leaving 9/10 of it. The process is carried out three times in all: the first litre swapped, the second, and one more. Chemical A left = 10 × (0.9)³ = 7.29 L, so B = 2.71 L, which is 27.1% of the 10 L, about 27%.
Why each option is right or wrong
- (a) Wrong: 25% would leave 7.5 L of A, not 7.29 L.
- (b) Right: 1 − 0.9³ = 0.271, about 27%.
- (c) Wrong: 29% does not match 1 − 0.9³.
- (d) Wrong: 31% does not match 1 − 0.9³.
Only the provisional key (27 May 2026) was found; the final key replaces it when found.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2026, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.