Question
A container contains 60 liters of a solution containing
25% alcohol. How many liters of pure alcohol must be added to make the alcohol concentration 40%?Solution
Let x liters of pure alcohol be added to the mixture. Initially, the amount of alcohol in the mixture is 25% of 60 liters, which is 15 liters. After adding x liters of pure alcohol, the total amount of alcohol becomes 15 + x liters, and the total volume of the solution becomes 60 + x liters. The final concentration of alcohol is 40%. We can set up the equation: (15 + x) / (60 + x) = 40/100 = 2/5. Cross-multiply: 5 × (15 + x) = 2 × (60 + x), 75 + 5x = 120 + 2x, 5x - 2x = 120 - 75, 3x = 45, x = 45 / 3 = 15 liters. Correct option: c) 15 liters.
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