An alloy contains gold and silver in the ratio 5 : 8 and another alloy contains gold and silver in the ratio 5 : 3. If equal amount of both the alloys are melted together, then the ratio of gold and silver in the resulting alloy is ?

Options

A. a. 113/108
B. b. 105/103
C. c. 103/113
D. d. 108/115

Explanation

To find the ratio of gold and silver in the resulting alloy when two alloys are melted together, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Ratios of Gold and Silver in Each Alloy:**
- The first alloy has gold and silver in the ratio of 5:8.
- The second alloy has gold and silver in the ratio of 5:3.

2. **Assume Equal Amounts of Each Alloy:**
- Let's assume we take 1 kg of each alloy for simplicity.

3. **Calculate the Amount of Gold and Silver in the First Alloy:**
- Total parts in the first alloy = 5 (gold) + 8 (silver) = 13 parts.
- Amount of gold in the first alloy = (5/13) * 1 kg = 5/13 kg.
- Amount of silver in the first alloy = (8/13) * 1 kg = 8/13 kg.

4. **Calculate the Amount of Gold and Silver in the Second Alloy:**
- Total parts in the second alloy = 5 (gold) + 3 (silver) = 8 parts.
- Amount of gold in the second alloy = (5/8) * 1 kg = 5/8 kg.
- Amount of silver in the second alloy = (3/8) * 1 kg = 3/8 kg.

5. **Combine the Amounts of Gold and Silver from Both Alloys:**
- Total gold = (5/13) kg + (5/8) kg.
- Total silver = (8/13) kg + (3/8) kg.

6. **Find a Common Denominator to Add the Fractions:**
- For gold: The common denominator of 13 and 8 is 104.
- Convert (5/13) to (40/104) and (5/8) to (65/104).
- Total gold = (40/104) + (65/104) = (105/104) kg.
- For silver: The common denominator of 13 and 8 is also 104.
- Convert (8/13) to (64/104) and (3/8) to (39/104).
- Total silver = (64/104) + (39/104) = (103/104) kg.

7. **Calculate the Ratio of Gold to Silver in the Resulting Alloy:**
- The ratio of gold to silver = Total gold : Total silver = (105/104) : (103/104).
- Simplifying this gives us the ratio of gold to silver = 105 : 103.

### Final Answer:
The ratio of gold to silver in the resulting alloy is **105 : 103**.