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 milk and water?
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