In a mixture of 126 kg of milk and water, milk and water are in the ratio 5 : 2. How much water must be added to the mixture to make this ratio 3 : 2 ?

Let water be x kg so milk = (126 - x) kg.

According to question,

$\Rightarrow \dfrac{126 - x}{x} = \dfrac{5}{2} \\[1em] \Rightarrow 2(126 - x) = 5x \\[1em] \Rightarrow 252 - 2x = 5x \\[1em] \Rightarrow 7x = 252 \\[1em] \Rightarrow x = 36.$

Water = 36 kg, Milk = 126 - 36 = 90 kg.

Let water to be added to make ratio 3 : 2 be y kg.

$\therefore \dfrac{90}{36 + y} = \dfrac{3}{2} \\[1em] \Rightarrow 180 = 3(36 + y) \\[1em] \Rightarrow 180 = 108 + 3y \\[1em] \Rightarrow 3y = 72 \\[1em] \Rightarrow y = 24.$

Hence, 24 kg of water must be added to the mixture to make this ratio 3 : 2.