A vessel contains 64 litres of mixture of milk and water in the ratio 7 : 3 respectively. 8 litres of mixture is replaced by 8 litres of milk. What is the ratio of milk and water in the resulting mixture ?

Solution of milk and water in vessel = 64 litres

ration of Milk:Water = 7:3

using

$$\frac{water concentration final}{total} = \frac{initial water conc.}{total}(1- \frac{removed volume}{total})^n$$

$$\frac{water concentration final}{total} = \frac{3}{10}(1- \frac{8}{64})^1$$

$$\frac{water concentration final}{total} = \frac{3}{10}(1- \frac{1}{8})^n$$

$$\frac{water concentration final}{total} = \frac{21}{80}$$

water : milk in new solution after replacement = 21: 59