CAT 2024 Slot 1 QA Q17 Ratio, Mixtures & Averages

Question 17 of the Quantitative Ability (QA) section, CAT 2024 Slot 1, with CAT's official answer and a worked solution.

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
  1. A
    1 : 27
  2. B
    1 : 81
  3. C
    1 : 26
  4. D
    1 : 80

Answer: (D) 1 : 80 Ratio, Mixtures & Averages MCQ

Solution

  1. Each operation keeps \(\frac13\) of the milk present.
  2. The process happens 4 times in all (once + three repeats): milk left \(= \left(\frac13\right)^4 = \frac{1}{81}\) of the glass.
  3. Water \(= \frac{80}{81}\), so milk : water \(= 1 : 80\).

Same concept in other years

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

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