In two alloys the ratio of Iron and copper is 4:3 and 6:1 respectively. If 14 kg of the first alloy and 42 kg of the second alloy are mixed together to form a new alloy, then what will be the ratio of copper to iron in the new alloy:

Options

A. `11:3`
B. `11:8`
C. `8:11`
D. None of these

Answer

To solve the problem, we need to find the ratio of copper to iron in the new alloy formed by mixing two alloys. Let's break down the solution step by step.

### Step 1: Determine the composition of Alloy 1
The ratio of iron to copper in Alloy 1 is 4:3. This means for every 4 parts of iron, there are 3 parts of copper.

- Total parts = 4 (iron) + 3 (copper) = 7 parts
- Total weight of Alloy 1 = 14 kg

Now, we can find the weight of each part:
- Weight of 1 part = Total weight / Total parts = 14 kg / 7 = 2 kg

Now we can calculate the weight of iron and copper in Alloy 1:
- Weight of iron in Alloy 1 = 4 parts × 2 kg/part = 8 kg
- Weight of copper in Alloy 1 = 3 parts × 2 kg/part = 6 kg

### Step 2: Determine the composition of Alloy 2
The ratio of iron to copper in Alloy 2 is 6:1. This means for every 6 parts of iron, there is 1 part of copper.

- Total parts = 6 (iron) + 1 (copper) = 7 parts
- Total weight of Alloy 2 = 42 kg

Now, we can find the weight of each part:
- Weight of 1 part = Total weight / Total parts = 42 kg / 7 = 6 kg

Now we can calculate the weight of iron and copper in Alloy 2:
- Weight of iron in Alloy 2 = 6 parts × 6 kg/part = 36 kg
- Weight of copper in Alloy 2 = 1 part × 6 kg/part = 6 kg

### Step 3: Combine the two alloys
Now, we will combine the weights of iron and copper from both alloys.

- Total weight of copper = Copper from Alloy 1 + Copper from Alloy 2
- Total weight of copper = 6 kg (from Alloy 1) + 6 kg (from Alloy 2) = 12 kg

- Total weight of iron = Iron from Alloy 1 + Iron from Alloy 2
- Total weight of iron = 8 kg (from Alloy 1) + 36 kg (from Alloy 2) = 44 kg

### Step 4: Find the ratio of copper to iron in the new alloy
Now, we can find the ratio of copper to iron in the new alloy:
- Ratio of copper to iron = Total weight of copper : Total weight of iron = 12 kg : 44 kg

To simplify this ratio:
- Divide both sides by 4:
- 12 ÷ 4 = 3
- 44 ÷ 4 = 11

Thus, the ratio of copper to iron in the new alloy is **3:11**.

### Final Answer
The ratio of copper to iron in the new alloy is **3:11**.

---