Question
A container has 40 litres of a solution which contains
25% acid. How many litres of a 50% acid solution must be added so that the resulting mixture has 40% acid?Solution
Quantity of acid in 40 L = 25% of 40 = (25/100) × 40 = 10 L Let x litres of 50% acid solution be added. Acid added = 50% of x = x/2 Total acid = 10 + x/2 Total volume = 40 + x We want 40% acid: (10 + x/2) / (40 + x) = 40/100 = 2/5 Cross multiply: 5(10 + x/2) = 2(40 + x) 50 + (5x/2) = 80 + 2x Multiply by 2 to clear fraction: 100 + 5x = 160 + 4x 5x − 4x = 160 − 100 x = 60 Answer: 60 litres of 50% solution.
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