Question
Two alloys A and B are made of copper and zinc only. In
alloy A, copper and zinc are in the ratio 3 : 5. In alloy B, they are in the ratio 7 : 5. How many kilograms of alloy B must be mixed with 16 kg of alloy A so that the resulting alloy has 55% copper by weight?Solution
ATQ, In alloy A, copper fraction = 3/(3+5) = 3/8. In 16 kg of A, copper = 16 × 3/8 = 6 kg. Let x kg of alloy B be added. In alloy B, copper fraction = 7/(7+5) = 7/12. Copper in x kg of B = x × 7/12. Total copper = 6 + (7x/12). Total mass = 16 + x. Required copper % = 55% ⇒ (6 + 7x/12) / (16 + x) = 0.55 Multiply both sides by 12: (72 + 7x) / (16 + x) = 6.6 72 + 7x = 6.6(16 + x) 72 + 7x = 105.6 + 6.6x 7x − 6.6x = 105.6 − 72 0.4x = 33.6 ⇒ x = 84 kg.
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