CAT 2024 Question Paper | Quant Slot 1

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 17 :A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is

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Video Explanation

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Explanatory Answer

Final concentration of milk \(=\) Initial concentration * \((1-(x / v))^n\)
\(x=\) volume replaced
\(v =\) total volume
\(n =\) number of iterations
Let initial quantity of milk \(= y\) litres
Final concentration \(=y(1-2 / 3)^4=y(1 / 3)^4=1 / 81 y\)
Volume of milk \(=1 / 81 y\)
Volume of water \(=y-(1 / 81 y)=80 / 81 y\)
Final ratio of milk to water in the glass \(=1: 80\)

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The question is "A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is"

Hence, the answer is '1 : 80'

Choice D is the correct answer.

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