UPSC Prelims 2026 CSAT, question 79

Topic: Arithmetic

Q79

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) 27Correct answer
(c) 29
(d) 31

Solution.

Answer: (b) 27

Starting with $10$ litres of chemical $A$ , each replacement of $1$ litre removes $\frac{1}{10}$ of the existing chemical $A$ , multiplying the volume of $A$ by $0.9$ .
After $3$ replacements, the volume of chemical $A$ remaining is $10 \times (0.9)^3 = 7.29$ litres, so the volume of chemical $B$ present is $10 - 7.29 = 2.71$ litres.
As a percentage of the $10$ -litre container, chemical $B$ is $\frac{2.71}{10} \times 100\% = 27.1\% \approx 27\%$ .