Question
Two different alloys contain steel and aluminum in the
ratios of 11:4 and 2:13, respectively. In what proportion should these two alloys be combined to achieve a final mixture with a steel-to-aluminum ratio of 9:11?Solution
Let both the alloys are mixed in the ratio of 1 : n kg.Hence total steel in the resulting alloy = (11/15 + 2n/15) kg = (11 + 2n)/15 kgAnd total aluminum = 1 + n - (11+2n)/15 = 4/15 + 13n/15 = (4 + 13n)/15So, (11 + 2n)/15 : (4 + 13n)/15 = 9 : 11=> 11 (11 + 2n) = 9 (4 + 13n)=> 121 + 22n = 36 + 117n=> 85 = 95n=> n = 17 / 19Hence required ratio = 1 : (17/19) = 19 : 17
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