Multiple choice

Alloy 'A' contains 60% zinc, 25% copper and 15% tin. Alloy 'B' contains 70% zinc, 20% copper and 10% tin. These two alloys are mixed together such that the resultant alloy contains 12% tin. What is the ratio of zinc to copper in the resultant alloy?

  1. 2 : 1

  2. 3 : 1

  3. 4 : 3

  4. 5 : 3

  5. 5 : 2
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B Correct answer
Explanation

Let x and y be the amounts of alloy A and B. Tin: 0.15x + 0.10y = 0.12(x+y). 0.03x = 0.02y, so x/y = 2/3. Zinc: 0.60x + 0.70y = 0.60(2) + 0.70(3) = 1.2 + 2.1 = 3.3. Copper: 0.25x + 0.20y = 0.25(2) + 0.20(3) = 0.5 + 0.6 = 1.1. Ratio of zinc to copper = 3.3 / 1.1 = 3:1.

AI explanation

Using the rule of alligation on the tin percentages of the two alloys, we write the values 15 and 10 on the left and right, and the target mean of 12 in the middle. This yields the ratio of alloy A to alloy B as (12 minus 10) to (15 minus 12), which equals 2 to 1. This means the mixture consists of 2 parts of alloy A and 1 part of alloy B. The resultant mixture therefore contains (2 times 60 percent) plus (1 times 70 percent) equals 190 percent zinc across three parts, giving a zinc concentration of 190 divided by 3. The copper concentration is (2 times 25 percent) plus (1 times 20 percent) equals 70 percent across three parts, yielding 70 divided by 3. The ratio of zinc to copper is therefore 190 divided by 3 to 70 divided by 3, which simplifies to 190 to 70, resulting in a final ratio of 3 to 1.

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