Multiple choice

Two alloys A and B contain gold and copper in the ratios of 2 : 3 and 3 : 7 by mass, respectively. Equal masses of alloys A and B are melted to make an alloy C. The ratio of gold to copper in alloy C is _____.

  1. 5 : 10

  2. 7 : 13

  3. 6 : 11

  4. 9 : 13
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B Correct answer
Explanation

Alloy A has gold/copper ratio 2:3 (2/5 gold). Alloy B has 3:7 (3/10 gold). Equal masses mean we average the fractions: (2/5 + 3/10) / 2 = (7/10) / 2 = 7/20 gold. Copper is 1 - 7/20 = 13/20. The ratio is 7:13.

AI explanation

Assume 100 grams of each alloy are mixed, so alloy A provides 40 grams of gold and 60 grams of copper, while alloy B provides 30 grams of gold and 70 grams of copper. Adding these masses gives a total of 70 grams of gold and 130 grams of copper in alloy C. Therefore, the required ratio of gold to copper is 7 : 13.

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