A and B are two alloys of gold and copper prepared by mixing metals in ratios 7:2 and 7:11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be:

Options

A. `7:5`
B. `5:9`
C. `9:5`
D. `5:7`

Answer

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

### Step 1: Understand the Ratios of Alloys A and B
- Alloy A is composed of gold and copper in the ratio 7:2.
- Alloy B is composed of gold and copper in the ratio 7:11.

### Step 2: Determine the Total Parts in Each Alloy
- For Alloy A:
- Total parts = 7 (gold) + 2 (copper) = 9 parts.
- For Alloy B:
- Total parts = 7 (gold) + 11 (copper) = 18 parts.

### Step 3: Equal Quantities of Alloys A and B
Since we need to take equal quantities of both alloys to form Alloy C, we can assume we take a common quantity that is a multiple of the total parts of both alloys. The least common multiple (LCM) of 9 and 18 is 18.

### Step 4: Calculate the Quantities of Gold and Copper in Alloy A
- If we take 18 parts of Alloy A:
- Gold in Alloy A = (7/9) * 18 = 14 parts.
- Copper in Alloy A = (2/9) * 18 = 4 parts.

### Step 5: Calculate the Quantities of Gold and Copper in Alloy B
- If we take 18 parts of Alloy B:
- Gold in Alloy B = (7/18) * 18 = 7 parts.
- Copper in Alloy B = (11/18) * 18 = 11 parts.

### Step 6: Combine the Quantities to Form Alloy C
- Total Gold in Alloy C = Gold from Alloy A + Gold from Alloy B = 14 + 7 = 21 parts.
- Total Copper in Alloy C = Copper from Alloy A + Copper from Alloy B = 4 + 11 = 15 parts.

### Step 7: Find the Ratio of Gold to Copper in Alloy C
- The ratio of Gold to Copper in Alloy C = Total Gold : Total Copper = 21 : 15.
- Simplifying the ratio by dividing both parts by 3 gives us:
- Ratio = 7 : 5.

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

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