Initial Mixture Analysis

The total volume of the milk and water mixture is 80 litres.

The initial ratio of milk to water is given as 7 : 3.

To find the initial quantities, calculate the total number of parts in the ratio:

Total parts = $ 7 + 3 = 10 $

Calculate the initial amount of milk:

Amount of Milk = $ \frac{7}{10} \times 80 \text{ litres} = 56 \text{ litres} $

Calculate the initial amount of water:

Amount of Water = $ \frac{3}{10} \times 80 \text{ litres} = 24 \text{ litres} $

Target Ratio Calculation

Water is added to the mixture to change the ratio to 2 : 1.

The amount of milk remains constant at 56 litres because only water is added.

Let $x$ represent the litres of water that need to be added.

The new amount of water in the mixture will be $ (24 + x) $ litres.

The desired new ratio of milk to water is 2 : 1.

Solving for Added Water

Set up an equation representing the new ratio:

$ \frac{\text{Amount of Milk}}{\text{New Amount of Water}} = \frac{2}{1} $

Substitute the known values:

$ \frac{56}{24 + x} = \frac{2}{1} $

Solve for $x$ by cross-multiplying:

$ 56 \times 1 = 2 \times (24 + x) $

$ 56 = 48 + 2x $

Subtract 48 from both sides:

$ 56 - 48 = 2x $

$ 8 = 2x $

Divide by 2:

$ x = \frac{8}{2} $

$ x = 4 $

Thus, 4 litres of water should be added.