Multiple choice

$A$ and $B$ are two alloys of gold and copper in the ratio $7 : 2$ and $7 : 11$ respectively. If equal quantities of these two alloys are melted to from a new alloy $C$, then the ratio of gold and copper in $C$ is $:$

  1. $6: 5$
  2. $9: 4$
  3. $12: 7$
  4. $7: 5$
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D Correct answer
Explanation

Alloy A: Gold/Copper = 7/9, 2/9. Alloy B: Gold/Copper = 7/18, 11/18. Equal quantities: (7/9 + 7/18) / (2/9 + 11/18) = (14/18 + 7/18) / (4/18 + 11/18) = 21/15 = 7/5.

AI explanation

Let x be the equal quantity of each alloy melted to form alloy C. Alloy A contains 7/9 gold and 2/9 copper, while alloy B contains 7/18 gold and 11/18 copper. The new alloy C has a gold to copper ratio of (7x/9 + 7x/18) to (2x/9 + 11x/18). Finding a common denominator gives the ratio of 21x/18 to 15x/18, which simplifies by dividing both sides by 3x/18 to 7 to 5. The ratio of gold to copper in alloy C is 7 to 5.

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