CAT 2024 Question Paper | Quant Slot 3

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 10 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

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Video Explanation

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Explanatory Answer

Initial quantity of water in the container \(=x\)
So, initial quantity of milk in the container \(=300-x\)
Part of mixture taken out \(=\frac{2 x}{300}\)
Part of mixture that is retained \(=1-\frac{2 x}{300}\)
So, part of milk that is retained \(=(300-x)\left(1-\frac{2 x}{300}\right)\)
Also, quantity of milk that is retained after the iteration \(=72 \%\) of \(300=216\)
Then,
\[ \begin{array}{l} (300-x)\left(1-\frac{2 x}{300}\right)=216 \\ 90000-300 x-600 x+2 x^2=216 \times 300 \\ 2 x^2-900 x+25200=0 \\ x^2-450 x+12600=0 \\ (x-420)(x-30)=0 \\ x=420 \text { (or) } x=30 \end{array} \] The total content itself 300 litre. So, \(x=420\) is inadmissible.
Thus, amount of water that was initially poured = 30 litre

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The question is "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"

Hence, the answer is '30'

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