Multiple choice

2 alloys containing copper and iron are in the ratio 5 : 9 and 4 : 3. If they are melted in equal quantities, then the ratio of copper to iron in the resultant alloy will be

  1. 9 : 12

  2. 13 : 15

  3. 17 : 18

  4. 40 : 51
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B Correct answer
Explanation

Alloy 1: 5/14 copper, 9/14 iron. Alloy 2: 4/7 copper, 3/7 iron. Equal quantities: (5/14 + 4/7) : (9/14 + 3/7) = (5/14 + 8/14) : (9/14 + 6/14) = 13/14 : 15/14 = 13 : 15.

AI explanation

When equal quantities of the two alloys are melted together, the resulting ratio is the sum of their respective parts. The parts of copper in the first alloy are 5 out of 14, and in the second alloy are 4 out of 7, or 8 out of 14. The parts of iron in the first alloy are 9 out of 14, and in the second alloy are 3 out of 7, or 6 out of 14. Adding these together, the total copper is 5 plus 8, giving 13 parts, and the total iron is 9 plus 6, giving 15 parts, making the final ratio 13 : 15.

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