Question
How many litres of a 20% alcohol solution must be mixed
with 30 litres of a 50% alcohol solution so that the resulting mixture has 40% alcohol?Solution
Let x litres of 20% solution be added. Alcohol in 20% solution = (20/100)x = x/5 Alcohol in 30 L of 50% solution = (50/100) × 30 = 15 L Total alcohol in mixture = x/5 + 15 Total volume = x + 30 Required concentration = 40% ⇒ (x/5 + 15) / (x + 30) = 40/100 = 2/5 Cross multiply: 5(x/5 + 15) = 2(x + 30) x + 75 = 2x + 60 75 − 60 = 2x − x x = 15 Answer: 15 litres of 20% solution.
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