Milk and water replacement

Question

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 $16 : 9$, then the capacity of the container, in litres, is

Accepted Answer

45. Let the total capacity of the container be $V$ litres. Initially, it contains only milk. After 2 operations, the fraction of milk remaining is: $$\frac{	ext{Final Milk}}{	ext{Total Capacity}} = \left(1 - \frac{9}{V}ight)^2$$ Given ratio of milk to water is $16 : 9$, so the ratio of milk to total volume is $\frac{16}{16 + 9} = \frac{16}{25}$. Therefore: $$\left(1 - \frac{9}{V}ight)^2 = \frac{16}{25}$$ $$1 - \frac{9}{V} = \frac{4}{5}$$ $$\frac{9}{V} = \frac{1}{5} \implies V = 45	ext{ litres.}$$

Answer

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Milk and water replacement

Explanation

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