Question

A certain amount of water was poured into a 300 litre container and the remaining portion of the container was filled with milk. Then an amount of this solution was taken out from the container which was twice the volume of water that was earlier poured into it, and water was poured to refill the container again. If the resulting solution contains 72% milk, then the amount of water, in litres, that was initially poured into the container was

Answer 1

Correct Answer: 30

Let $x$ litres be the initial amount of water. The container holds 300 litres in total, so the initial amount of milk is $300 - x$ litres.
When a volume of solution twice the initial water amount is removed, the volume removed is $2x$ litres.Nbsp;

Because the solution is uniform, the proportion of water in the removed volume is $\frac{x}{300}$, and the proportion of milk is $\frac{300-x}{300}$.Nbsp;

Amount of water removed: $\frac{x}{300} \times 2x = \frac{2x^2}{300}$.Nbsp;

Amount of milk removed: $\frac{300-x}{300} \times 2x = \frac{2x(300-x)}{300}$.

After removing the solution, water is added to refill the container. The new total amount of water is:
\[ x - \frac{2x^2}{300} + x = 2x - \frac{2x^2}{300} \]

The total amount of milk remaining in the container is:
\[ 300 - x - \frac{2x(300-x)}{300} \]

After refilling, the total volume is 300 litres, and the solution is now 72% milk.
\[ 0.72 \times 300 = 216 \text{ litres of milk} \]

Set the remaining milk equal to 216 litres:
\[ 300 - x - \frac{2x(300-x)}{300} = 216 \]

Solving this equation for $x$ yields:
\[ x = 30 \]
Therefore, the initial amount of water poured into the container was 30 litres.