Question
A certain quantity of a 35% sugar solution is mixed with
8 liters of a 48% sugar solution to obtain a 40% sugar solution. How many liters of the 35% sugar solution was there in the mixture?Solution
Let Q liters of a 35% sugar solution be mixed with 8 liters of a 48% sugar solution to obtain a 40% sugar. In Q liters, the quantity of sugar = Q × 35% = 0.35Q liters In 8 liters, the quantity of sugar = 8 × 48% = 8 × 0.48 = 3.84 liters According to the question, 0.35Q + 3.84 = (8 + Q) × 40% 0.35Q + 3.84 = (8 + Q) × 0.4 0.35Q + 3.84 = 3.2 + 0.4Q 0.4Q - 0.35Q = 3.84 - 3.2 0.05Q = 0.64 Q=.64/.05 Q=12.8 liters
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