NinetynineCAT 2024 Slot 3 QA Q10 Ratio, Mixtures & Averages
Question 10 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.
A certain amount of water was poured into a 300 litre container and the remaining portion of the container was filled with milk. Then an amount of this solution was taken out from the container which was twice the volume of water that was earlier poured into it, and water was poured to refill the container again. If the resulting solution contains 72% milk, then the amount of water, in litres, that was initially poured into the container was
TITA: type in the answer. There are no options and no negative marking.
Answer: 30 Ratio, Mixtures & Averages TITA
Solution
- Water \(w\), milk \(300 - w\). Removing \(2w\) of mix and refilling with water leaves milk \((300 - w)\cdot\frac{300 - 2w}{300}\).
- Set equal to \(0.72 \times 300 = 216\): \((300 - w)(300 - 2w) = 64800 \Rightarrow w^2 - 450w + 12600 = 0\).
- \(w = 30\) or \(420\); only 30 fits in the 300 L container.