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    Question

    A mixture contains alcohol and water in the ratio 7:3.

    If 15 liters of water is added to the mixture, the ratio becomes 7:5. What is the initial quantity of alcohol in the mixture?
    A 42 liters Correct Answer Incorrect Answer
    B 52.5 liters Correct Answer Incorrect Answer
    C 56 liters Correct Answer Incorrect Answer
    D 63.5 liters Correct Answer Incorrect Answer

    Solution

    Let the initial quantities of alcohol and water be 7x and 3x liters, respectively. After adding 15 liters of water, the ratio becomes 7:5. (7x) / (3x + 15) = 7 / 5. Cross multiply: 5(7x) = 7(3x + 15). 35x = 21x + 105. 35x - 21x = 105 14x = 105. x = 105 / 14 = 7.5. Initial quantity of alcohol = 7x = 7 Ă— 7.5 = 52.5 liters. Correct option: b

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