Sarah had a container of homemade lemonade that she had prepared. Initially, the lemonade contained 25% lemon juice, and the rest was water. She decided to share some of the lemonade with her friend and replaced it with another batch of lemonade, in which the lemon juice content was only 10%. After mixing, the new lemonade was tested and found to contain 15% lemon juice, with the rest being water. What proportion of the original lemonade did Sarah replace with the other batch of lemonade?

Using the rule of alligation with the given concentrations, the ratio of the original lemonade kept to the new lemonade replaced is (15 - 10) : (25 - 15). This simplifies to 5 : 10, which equals 1 : 2. Inverting this ratio to find the proportion of the original lemonade that was replaced gives 2 : 3.

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