CAT 2023 Question Paper | Quant Slot 2

CAT Questions

CAT 2023 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 14 : A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is

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Video Explanation

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Explanatory Answer

Every time 10% of the mixture is replace with a pure adulterant (here water), the concentration of the mixture becomes 90% of the initial concentration.
Similarly when a proportion p of a mixture is replaced with pure adulterant, the concentration of the mixture becomes (1 - p) times the previous concentration. (0 ≤ p ≤ 1)
Here p = \( \frac { 4 } { 40 } = 0.1 \)
Initially there was pure milk, so the strength of the mixture is 100% or 1 (in terms of proportion)
After repeating the process n times the concentration of Milk in the mixture will be \( 1 \times 0.9 ^ { n } \)
For the volume of milk to be less than the volume of water, p should be less than 0.5
So we are looking for the smallest n, such that \( 1 \times 0.9 ^ { n } < 0.5 \)
This happens when n = 7
(You can check this by trial and error)

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The question is " A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is "

The answer is '7'

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