NinetynineCAT 2023 Slot 2 QA Q14 Ratio, Mixtures & Averages
Question 14 of the Quantitative Ability (QA) section, CAT 2023 Slot 2, with CAT's official answer and a worked solution.
A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is
TITA: type in the answer. There are no options and no negative marking.
Answer: 7 Ratio, Mixtures & Averages TITA
Solution
- Each replacement keeps \(\frac{36}{40} = 0.9\) of the milk, so after \(n\) times milk \(= 40(0.9)^n\).
- Milk is less than water when milk \(< 20\), i.e. \(0.9^n < 0.5\).
- \(0.9^6 \approx 0.531\) and \(0.9^7 \approx 0.478\), so the smallest \(n\) is 7.