How much water must be added to $14$ kilolitres of milk worth $54$ P. a litre so that the value of the mixture may be $42$ P. a litre?

Using the rule of mixture or alligation, the cost of pure milk is 54 paise per liter and the cost of added water is 0 paise per liter to achieve a mixture worth 42 paise per liter. The ratio of the quantity of milk to water is the difference between the mean price and the water price to the difference between the milk price and the mean price, which is 42 to 12, or 7 to 2. Since 7 parts represent the 14 kilolitres of milk, 1 part equals 2 kilolitres; therefore, the 2 parts of water equal 4 kilolitres. The result is 4 k lit.

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