From a container 64 litres of pure milk, 8 litres of milk is replaced with water. This process is repeated again. What is the ratio between…

Initially, in the container amount of milk = 64 litres

Amount of water = 0 litres

First, 8 litres of milk is replaced

∴ Amount of milk = 64 - 8 = 56 litres

Amount of water = 8 litres

Ratio of milk and water = 56 ? 8 = 7 ? 1

Second, 8 litres of mixture is replaced

In this mixture, ratio of milk and water is = 7 ? 1

Thus, amount of milk replaced = $(\frac{7}{8} \times 8 = 7)$ litres

Amount of milk remaining = 56 - 7 = 49 litres

Amount of water = 64 - 49 = 15 litres

Now new ratio = 49 ? 15

Alternate method :

To find amount of milk

$({\rm{Original\;amount\;}}{\left( {1 - \;\frac{{Amount\;replaced\;by\;water}}{{Original\;amount}}} \right)^n})$

Where n = number of operations

$(64{\left( {1 - \;\frac{8}{{64}}} \right)^2} = 49)$ litres

Amount of water = 64 - 49 = 15 litres

Now new ratio = 49 ? 15