In a mixture of 45 litres, the ratio of milk to water is 13 : 2. How much water must be added to this mixture to make the ratio of milk to water as 3 : 1?

Ratio of milk to water = 13 : 2.

Total quantity of mixture = 45 litres

Sum of ratio = 13 + 2 = 15.

Quantity of milk = $\dfrac{13}{15}$ x 45 = 13 x 3 = 39 litres.

Quantity of water = $\dfrac{2}{15}$ x 45 = 2 x 3 = 6 litres.

Let the water added be x litres, so quantity of water = (6 + x) litres.

Now ratio = 3 : 1

$\therefore \dfrac{39}{6 + x} = \dfrac{3}{1} \\[0.5em] \Rightarrow 39 = 3(6 + x) \\[0.5em] \Rightarrow 39 = 18 + 3x \\[0.5em] \Rightarrow 3x = 39 - 18 \\[0.5em] \Rightarrow x = \dfrac{21}{3} \\[0.5em] \Rightarrow x = 7.$

The water that must be added is 7 litres.