Question
A solution contains alcohol and water in the ratio 3:2. If 15 liters of water is added to the solution, the ratio becomes 3:5. What was the initial volume of the solution?
Solution
Let the initial volumes of alcohol and water be 3x and 2x respectively. Total initial volume = 3x + 2x = 5x. After adding 15 liters of water, the new volume of water = 2x + 15. New ratio: 3x / (2x + 15) = 3/5. Cross-multiplying gives: 15x = 6x + 45 → 9x = 45 x = 5. Total initial volume = 5x = 5 * 5 = 25 liters.
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