Initial Mixture Quantities

The total volume of the mixture is 460 litres.

The initial ratio of milk to water is 11:12.

Calculate the total parts in the ratio: $11 + 12 = 23$ parts.

Determine the volume represented by one part: $\frac{460 \text{ litres}}{23 \text{ parts}} = 20 \text{ litres/part}$.

Calculate the initial quantity of milk: $11 \text{ parts} \times 20 \text{ litres/part} = 220 \text{ litres}$.

Calculate the initial quantity of water: $12 \text{ parts} \times 20 \text{ litres/part} = 240 \text{ litres}$.

Calculating Added Milk for New Proportion

Let the amount of milk to be added be $x$ litres.

After adding milk, the new quantity of milk will be $220 + x$ litres.

The quantity of water remains unchanged at $240$ litres.

The required new ratio of milk to water is 3:2.

Set up the equation based on the new ratio:

$ \frac{\text{New Milk Quantity}}{\text{Water Quantity}} = \frac{3}{2} $

$ \frac{220 + x}{240} = \frac{3}{2} $

Solving the Equation

To solve for $x$, cross-multiply:

$ 2 \times (220 + x) = 3 \times 240 $

$ 440 + 2x = 720 $

Subtract 440 from both sides:

$ 2x = 720 - 440 $

$ 2x = 280 $

Divide by 2 to find $x$:

$ x = \frac{280}{2} $

$ x = 140 $

Thus, 140 litres of milk must be added.