CAT 2023 Question Paper | Quant Slot 1

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 11 : A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with same amount of cocoa powder to form a new mixture Q. If the ratio of coffee and cocoa in the mixture Q is 16 : 9, then the ratio of cocoa in mixture P to that in mixture Q is

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Video Explanation

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Explanatory Answer

Every time 20% of the mixture is replace with a pure adulterant (here cocoa), the concentration of the mixture becomes 80% 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)
Initially there was pure coffee, so the strength of the mixture is 100% or 1 (in terms of proportion)
Let a proportion p of the mixture be replaced each time… Since after repeating the process twice, we have the concentration of coffee as \( \frac { 16 } { 16 + 9 } = \frac { 16 } { 25 } \) at the end of the two replacements.
∴ \( ( 1 - p ) ^ { 2 } = \frac { 16 } { 25 } \)
\( 1 - p = \frac { 4 } { 5 } \)
p = \( \frac { 1 } { 5 } \)
Or, 20% of the mixture is replaced each time.
The ratio of cocoa powder in the mixture P and Q will then be \( \frac { \frac { 1 } { 5 } } { \frac { 9 } { 25 } } = \frac { 5 } { 9 } \) .
Therefore, the ratio is 5 : 9

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The answer is '5 : 9'

Choice C is the correct answer.