CAT 2025 Question Paper | Quant Slot 3

CAT Questions

CAT 2025 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 22 : 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

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Video Explanation

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Explanatory Answer

Let the volume initially taken from Vessel A be \(x\) litres.

First Transfer (Vessel A to Vessel B):
Vessel A initially contains 60 litres of pure alcohol.
After removing \(x\) litres:
\[ \text{Alcohol in A}=60-x \]

Vessel B initially contains 60 litres of pure water.
After adding \(x\) litres of alcohol:
\[ \text{Total liquid in B}=60+x \]

Second Transfer (Vessel B to Vessel A):
The same \(x\) litres of mixed liquid are transferred back to A.

Concentration of water in B:
\[ \frac{60}{60+x} \]
Water transferred back to A:
\[ \frac{60x}{60+x} \]

Concentration of alcohol in B:
\[ \frac{x}{60+x} \]
Alcohol transferred back to A:
\[ \frac{x^2}{60+x} \]

Therefore, after the second transfer:
\[ \text{Water in A}=\frac{60x}{60+x} \]
\[ \text{Alcohol in A}=60-x+\frac{x^2}{60+x} \]

Given the resultant ratio of alcohol to water is \(15:4\):
\[ \frac{60-x+\frac{x^2}{60+x}} {\frac{60x}{60+x}} =\frac{15}{4} \]

Solving gives:
\[ x=16 \]

Therefore, the volume initially taken out from Vessel A is \(16\) litres.

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The answer is '16'

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