Mixture Replacement Iterations

CAT 2024 Slot 1 · QA · Easy · Mixtures and Alligations

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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

Explanation

In each step, 1−23=131 - \frac{2}{3} = \frac{1}{3} of the original milk remains. The operation is performed a total of 1+3=41 + 3 = 4 times.

Final fraction of milk=(13)4=181\text{Final fraction of milk} = \left(\frac{1}{3}\right)^4 = \frac{1}{81} Fraction of water=1−181=8081\text{Fraction of water} = 1 - \frac{1}{81} = \frac{80}{81} Ratio of milk to water=1:80\text{Ratio of milk to water} = 1 : 80

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