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

In 30L mixture (ratio 7:3):

Milk = $\frac{7}{10} × 30 = 21$ L

Water = $\frac{3}{10} × 30 = 9$ L

Let $x$ L of water be added

Total water = $(9 + x)$ L

Total mixture = $(30 + x)$ L

For 40% water:

$\frac{9 + x}{30 + x} = \frac{40}{100}$

$\Rightarrow (9 + x) = 0.4(30 + x)$

$\Rightarrow 9 + x = 12 + 0.4x$

$\Rightarrow 0.6x = 3$

$x = 5$

Therefore, 5 liters of water should be added.