68 kg of a mixture contains milk and water in the ratio 27 : 7. How much more water is to be added to this mixture to get a new mixture containing milk and water in the ratio 3 : 1?

Given,

Milk : Water = 27 : 7 and total = 68 kg

Milk = $\dfrac{27}{27 + 7} \times 68 = \dfrac{27}{34} \times 68 = 54\text{ kg}$

Water = $\dfrac{7}{27 + 7} \times 68 = \dfrac{7}{34} \times 68 = 14\text{ kg}$

Let x kg of water be added to make the ratio of milk to water as 3 : 1.

$\Rightarrow \dfrac{54}{14 + x} = \dfrac{3}{1} \\[1em] \Rightarrow 54 = 3(14 + x) \\[1em] \Rightarrow 54 = 42 + 3x \\[1em] \Rightarrow 54 - 42 = 3x \\[1em] \Rightarrow 12 = 3x \\[1em] \Rightarrow x = 4.$

Hence, 4 kg of water must be added.