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

Let the amount of water initially poured into the container be $x$ litres. Therefore, the amount of milk in the container is $300 - x$ litres, as the total volume is 300 litres.
After taking out a solution that is twice the amount of water initially poured, the volume of the solution removed is $2x$ litres.

Since the solution is homogeneous, the fraction of water in the removed solution is $\frac{x}{300}$ and the fraction of milk removed is $\frac{300-x}{300}$.

Water removed: $\frac{x}{300} \times 2x = \frac{2x^2}{300}$.

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

After the solution is removed, water is poured in to refill the container, so the total amount of water in the container becomes:
$x - \frac{2x^2}{300} + x = 2x - \frac{2x^2}{300}$

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

After refilling the container, the total volume of the solution remains 300 litres, and the resulting solution contains 72% milk.
$0.72 \times 300 = 216 \text{ litres of milk}$

Equating the amount of milk left in the container to 216:
$300 - x - \frac{2x(300-x)}{300} = 216$

Solving this equation for $x$, we get:
$x = 30$
Thus, the amount of water initially poured into the container is {30} litres.

Answer 2

Let the amount of water initially poured into the container be $x$ litres. Therefore, the amount of milk in the container is $300 - x$ litres, as the total volume is 300 litres.
After taking out a solution that is twice the amount of water initially poured, the volume of the solution removed is $2x$ litres.

Since the solution is homogeneous, the fraction of water in the removed solution is $\frac{x}{300}$ and the fraction of milk removed is $\frac{300-x}{300}$.

Water removed: $\frac{x}{300} \times 2x = \frac{2x^2}{300}$.

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

After the solution is removed, water is poured in to refill the container, so the total amount of water in the container becomes:
$x - \frac{2x^2}{300} + x = 2x - \frac{2x^2}{300}$

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

After refilling the container, the total volume of the solution remains 300 litres, and the resulting solution contains 72% milk.
$0.72 \times 300 = 216 \text{ litres of milk}$

Equating the amount of milk left in the container to 216:
$300 - x - \frac{2x(300-x)}{300} = 216$

Solving this equation for $x$, we get:
$x = 30$
Thus, the amount of water initially poured into the container is {30} litres.