A and B are two alloys of gold and copper prepared by mixing metals in the ratio 5:3 and 5: 11 respectively. Equal quantities of these alloys are melted to form a third alloy C. The ratio of gold and copper in the alloy C is

Options

A. `25:33`
B. `33:25`
C. `15:17`
D. `17:15`

Answer

To solve the problem, we need to determine the ratio of gold and copper in the third alloy C, formed by melting equal quantities of alloys A and B.

### Step-by-Step Solution:

1. **Identify the Ratios of Alloys A and B:**
- Alloy A is composed of gold and copper in the ratio of 5:3.
- Alloy B is composed of gold and copper in the ratio of 5:11.

2. **Assume Equal Quantities of Alloys:**
- Let’s assume we take 8 parts of each alloy (since the total parts in A is 5 + 3 = 8 and in B is 5 + 11 = 16, we can take a common multiple).
- Therefore, we will take 8 units of Alloy A and 16 units of Alloy B.

3. **Calculate the Amount of Gold and Copper in Alloy A:**
- In Alloy A (5 parts gold and 3 parts copper):
- Total parts = 5 + 3 = 8
- Gold in 8 units of Alloy A = (5/8) * 8 = 5 units
- Copper in 8 units of Alloy A = (3/8) * 8 = 3 units

4. **Calculate the Amount of Gold and Copper in Alloy B:**
- In Alloy B (5 parts gold and 11 parts copper):
- Total parts = 5 + 11 = 16
- Gold in 8 units of Alloy B = (5/16) * 16 = 5 units
- Copper in 8 units of Alloy B = (11/16) * 16 = 11 units

5. **Combine the Amounts to Form Alloy C:**
- Total gold in Alloy C = Gold from Alloy A + Gold from Alloy B = 5 + 5 = 10 units
- Total copper in Alloy C = Copper from Alloy A + Copper from Alloy B = 3 + 11 = 14 units

6. **Determine the Ratio of Gold to Copper in Alloy C:**
- The ratio of gold to copper in Alloy C = Gold : Copper = 10 : 14
- Simplifying this ratio gives us = 5 : 7.

### Final Answer:
The ratio of gold to copper in alloy C is **5:7**.