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?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 × 7.5 = 52.5 liters. Correct option: b
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