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A and B are two alloys of gold and copper prepared by mixing metals in proportions 5: 3 and 5: 11 respectively. If equal quantities of this alloys are melted to a third alloy C, what would be the proportion of gold and copper in the alloys thus formed?
- a)25: 33
- b)33: 25
- c)15: 17
- d)17: 15
- e)17: 16
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A and B are two alloys of gold and copper prepared by mixing metals in...
To find the proportion of gold and copper in the third alloy C formed by melting equal quantities of alloys A and B, we need to consider the individual proportions of gold and copper in each alloy.
Let's calculate the proportion of gold and copper in alloy A:
Gold: 5 parts out of (5 + 3) = 5/8
Copper: 3 parts out of (5 + 3) = 3/8
Gold: 5 parts out of (5 + 3) = 5/8
Copper: 3 parts out of (5 + 3) = 3/8
Similarly, let's calculate the proportion of gold and copper in alloy B:
Gold: 5 parts out of (5 + 11) = 5/16
Copper: 11 parts out of (5 + 11) = 11/16
Gold: 5 parts out of (5 + 11) = 5/16
Copper: 11 parts out of (5 + 11) = 11/16
Since we are melting equal quantities of alloys A and B, the proportions will be added together:
Gold in alloy C = (5/8) + (5/16) = 10/16 + 5/16 = 15/16
Copper in alloy C = (3/8) + (11/16) = 6/16 + 11/16 = 17/16
Copper in alloy C = (3/8) + (11/16) = 6/16 + 11/16 = 17/16
Therefore, the proportion of gold to copper in alloy C is 15:17.
The correct answer is C: 15:17.
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A and B are two alloys of gold and copper prepared by mixing metals in...
Understanding Alloys A and B
Alloy A consists of gold and copper in the ratio of 5:3. This means for every 8 parts of the alloy, 5 parts are gold and 3 parts are copper.
- **Gold in Alloy A**: \( \frac{5}{8} \)
- **Copper in Alloy A**: \( \frac{3}{8} \)
Alloy B has a gold to copper ratio of 5:11. Here, for every 16 parts of the alloy, 5 parts are gold and 11 parts are copper.
- **Gold in Alloy B**: \( \frac{5}{16} \)
- **Copper in Alloy B**: \( \frac{11}{16} \)
Equal Quantities of Alloys A and B
Assuming we take 1 unit of each alloy:
- **Gold from Alloy A**: \( \frac{5}{8} \)
- **Copper from Alloy A**: \( \frac{3}{8} \)
- **Gold from Alloy B**: \( \frac{5}{16} \)
- **Copper from Alloy B**: \( \frac{11}{16} \)
Calculating Total Gold and Copper in Alloy C
Now, we find the total gold and copper in the new alloy C:
1. **Total Gold**:
- From Alloy A: \( \frac{5}{8} \)
- From Alloy B: \( \frac{5}{16} \)
To add these, convert \( \frac{5}{8} \) to sixteenths:
- \( \frac{5}{8} = \frac{10}{16} \)
Therefore, total gold in Alloy C:
- \( \frac{10}{16} + \frac{5}{16} = \frac{15}{16} \)
2. **Total Copper**:
- From Alloy A: \( \frac{3}{8} \)
- From Alloy B: \( \frac{11}{16} \)
Again, convert \( \frac{3}{8} \):
- \( \frac{3}{8} = \frac{6}{16} \)
Thus, total copper in Alloy C:
- \( \frac{6}{16} + \frac{11}{16} = \frac{17}{16} \)
Final Ratio of Gold to Copper in Alloy C
The ratio of gold to copper in Alloy C is:
- Gold: \( \frac{15}{16} \)
- Copper: \( \frac{17}{16} \)
The final ratio is:
- **Gold: Copper = 15:17**
Thus, the correct answer is option **C** (15:17).
Alloy A consists of gold and copper in the ratio of 5:3. This means for every 8 parts of the alloy, 5 parts are gold and 3 parts are copper.
- **Gold in Alloy A**: \( \frac{5}{8} \)
- **Copper in Alloy A**: \( \frac{3}{8} \)
Alloy B has a gold to copper ratio of 5:11. Here, for every 16 parts of the alloy, 5 parts are gold and 11 parts are copper.
- **Gold in Alloy B**: \( \frac{5}{16} \)
- **Copper in Alloy B**: \( \frac{11}{16} \)
Equal Quantities of Alloys A and B
Assuming we take 1 unit of each alloy:
- **Gold from Alloy A**: \( \frac{5}{8} \)
- **Copper from Alloy A**: \( \frac{3}{8} \)
- **Gold from Alloy B**: \( \frac{5}{16} \)
- **Copper from Alloy B**: \( \frac{11}{16} \)
Calculating Total Gold and Copper in Alloy C
Now, we find the total gold and copper in the new alloy C:
1. **Total Gold**:
- From Alloy A: \( \frac{5}{8} \)
- From Alloy B: \( \frac{5}{16} \)
To add these, convert \( \frac{5}{8} \) to sixteenths:
- \( \frac{5}{8} = \frac{10}{16} \)
Therefore, total gold in Alloy C:
- \( \frac{10}{16} + \frac{5}{16} = \frac{15}{16} \)
2. **Total Copper**:
- From Alloy A: \( \frac{3}{8} \)
- From Alloy B: \( \frac{11}{16} \)
Again, convert \( \frac{3}{8} \):
- \( \frac{3}{8} = \frac{6}{16} \)
Thus, total copper in Alloy C:
- \( \frac{6}{16} + \frac{11}{16} = \frac{17}{16} \)
Final Ratio of Gold to Copper in Alloy C
The ratio of gold to copper in Alloy C is:
- Gold: \( \frac{15}{16} \)
- Copper: \( \frac{17}{16} \)
The final ratio is:
- **Gold: Copper = 15:17**
Thus, the correct answer is option **C** (15:17).
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