Milk and water replacement

CAT 2021 Slot 2 · QA · Medium · Mixtures

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From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16:916 : 9, then the capacity of the container, in litres, is

Answer

45

Explanation

Let the total capacity of the container be VV litres. Initially, it contains only milk.

After 2 operations, the fraction of milk remaining is: Final MilkTotal Capacity=(1−9V)2\frac{\text{Final Milk}}{\text{Total Capacity}} = \left(1 - \frac{9}{V}\right)^2

Given ratio of milk to water is 16:916 : 9, so the ratio of milk to total volume is 1616+9=1625\frac{16}{16 + 9} = \frac{16}{25}.

Therefore: (1−9V)2=1625\left(1 - \frac{9}{V}\right)^2 = \frac{16}{25} 1−9V=451 - \frac{9}{V} = \frac{4}{5} 9V=15  ⟹  V=45 litres.\frac{9}{V} = \frac{1}{5} \implies V = 45\text{ litres.}

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