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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