A and B are two alloy of tin and copper prepared by mixing metals in proportions `13: 11 and 5:7` respectively. If equal quantities of two alloys melted to form a 3rd alloy C, the proportion of tin and copper in C will be?

Options

A. `23:25`
B. `22:23`
C. `18:17`
D. `22:27`

Answer

To solve the problem step by step, we will analyze the proportions of tin and copper in the two alloys A and B, and then find the proportions in the new alloy C formed by mixing equal quantities of A and B.

### Step 1: Understand the proportions in Alloy A and Alloy B
- Alloy A has tin and copper in the ratio of 13:11.
- Alloy B has tin and copper in the ratio of 5:7.

### Step 2: Calculate the total parts in each alloy
- For Alloy A: Total parts = 13 + 11 = 24.
- For Alloy B: Total parts = 5 + 7 = 12.

### Step 3: Find the proportion of tin and copper in Alloy A
- Tin in Alloy A = 13 parts
- Copper in Alloy A = 11 parts

### Step 4: Find the proportion of tin and copper in Alloy B
- Tin in Alloy B = 5 parts
- Copper in Alloy B = 7 parts

### Step 5: Normalize the proportions to a common total
To mix equal quantities of A and B, we need to express both alloys in terms of the same total parts. The least common multiple of 24 (from Alloy A) and 12 (from Alloy B) is 24.

- For Alloy A (already 24 parts):
- Tin = 13 parts
- Copper = 11 parts

- For Alloy B (we need to scale it up to 24 parts):
- Scale factor = 24 / 12 = 2
- Tin in Alloy B = 5 * 2 = 10 parts
- Copper in Alloy B = 7 * 2 = 14 parts

### Step 6: Combine the two alloys in equal quantities
Now we mix equal quantities of A and B:
- Total Tin in Alloy C = Tin from A + Tin from B = 13 + 10 = 23 parts
- Total Copper in Alloy C = Copper from A + Copper from B = 11 + 14 = 25 parts

### Step 7: Write the final ratio of Tin to Copper in Alloy C
The ratio of Tin to Copper in Alloy C is:
- Tin : Copper = 23 : 25

### Conclusion
Thus, the proportion of tin and copper in the new alloy C is **23:25**.

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