How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it? 

$\frac{\mathrm{Milk}}{\mathrm{water}}=\frac{7}{3}\Rightarrow \frac{\mathrm{Milk}}{7}=\frac{\mathrm{water}}{3}=\mathrm{k}$

$7k+3k=30\Rightarrow k=7$

Quantity of milk =21

Quantity of water=9 

Let x litres of  water is added

$$\begin{gathered} \mathrm{Percentage} \mathrm{of} \mathrm{water}=\frac{\mathrm{x}+9}{\mathrm{x}+30}\times 100=40\Rightarrow 6\mathrm{x}=30 \\ \therefore \mathrm{x}=5 \end{gathered}$$

 5 litres of water should be added such that the resultant mixture has 40% water in it