CAT 2023 Slot 1 QA Q11 Ratio, Mixtures & Averages

Question 11 of the Quantitative Ability (QA) section, CAT 2023 Slot 1, with CAT's official answer and a worked solution.

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
  1. A
    4 : 9
  2. B
    1 : 3
  3. C
    5 : 9
  4. D
    1 : 2

Answer: (C) 5 : 9 Ratio, Mixtures & Averages MCQ

Solution

  1. If a fraction \(f\) is replaced each time, coffee left after two rounds is \((1-f)^2\) of the original.
  2. Coffee in Q is \(\frac{16}{25}\), so \(1-f = \frac45\) and \(f = \frac15\).
  3. Cocoa in P \(= \frac15 = \frac{5}{25}\); cocoa in Q \(= \frac{9}{25}\).
  4. Ratio \(= 5 : 9\).

Same concept in other years

See every question on Repeated replacement of a mixture: concentration × (1 − f) each time.

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