NinetynineCAT 2025 Slot 3 QA Q22 Ratio, Mixtures & Averages
Question 22 of the Quantitative Ability (QA) section, CAT 2025 Slot 3, with CAT's official answer and a worked solution.
Vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. A certain volume is taken out from A and poured into B. After stirring, the same volume is taken out from B and poured into A. If the resultant ratio of alcohol and water in A is 15 : 4, then the volume, in litres, initially taken out from A is
TITA: type in the answer. There are no options and no negative marking.
Answer: 16 Ratio, Mixtures & Averages TITA
Solution
- Let \(x\) litres move from A to B. B then holds \(x\) alcohol and 60 water.
- Taking \(x\) from B returns \(\frac{x^2}{60 + x}\) alcohol and \(\frac{60x}{60 + x}\) water to A.
- Alcohol in A: \(60 - x + \frac{x^2}{60 + x} = \frac{3600}{60 + x}\); water in A: \(\frac{60x}{60 + x}\). Ratio \(= \frac{60}{x}\).
- \(\frac{60}{x} = \frac{15}{4} \Rightarrow x = 16\).
Shortcut. Alcohol in A simplifies to \(\frac{3600}{60+x}\), so the ratio is just \(60 : x\).