Alloy A contains 40% gold and 60% silver. Alloy B contains 35% gold and 40% silver and 25% copper. Alloys A and B are mixed in the ratio of 1:4 .What is the ratio of gold and silver in the newly formed alloy is?

Options

A. A) 20% and 30%
B. B) 36% and 44%
C. C) 25% and 35%
D. D) 49% and 36%

Answer

To solve the problem step by step, we will analyze the composition of both alloys and then find the ratio of gold and silver in the newly formed alloy after mixing.

### Step 1: Determine the composition of Alloy A and Alloy B
- **Alloy A** contains:
- Gold: 40%
- Silver: 60%

- **Alloy B** contains:
- Gold: 35%
- Silver: 40%
- Copper: 25%

### Step 2: Assume weights for the alloys
Let's assume:
- Weight of Alloy A = 100 kg
- Weight of Alloy B = 400 kg

### Step 3: Calculate the amount of gold and silver in Alloy A
From Alloy A (100 kg):
- Amount of Gold = 40% of 100 kg = 40 kg
- Amount of Silver = 60% of 100 kg = 60 kg

### Step 4: Calculate the amount of gold and silver in Alloy B
From Alloy B (400 kg):
- Amount of Gold = 35% of 400 kg = 140 kg
- Amount of Silver = 40% of 400 kg = 160 kg

### Step 5: Combine the amounts from both alloys
Now, we will combine the amounts of gold and silver from both alloys:
- Total Gold = Gold from Alloy A + Gold from Alloy B
- Total Gold = 40 kg + 140 kg = 180 kg

- Total Silver = Silver from Alloy A + Silver from Alloy B
- Total Silver = 60 kg + 160 kg = 220 kg

### Step 6: Calculate the total weight of the new alloy
Total weight of the new alloy = Weight of Alloy A + Weight of Alloy B
- Total Weight = 100 kg + 400 kg = 500 kg

### Step 7: Find the ratio of gold to silver in the new alloy
Now, we need to find the ratio of gold to silver:
- Ratio of Gold to Silver = Total Gold : Total Silver
- Ratio = 180 kg : 220 kg

### Step 8: Simplify the ratio
To simplify the ratio, we can divide both sides by 20:
- Ratio = (180/20) : (220/20) = 9 : 11

### Final Answer
The ratio of gold to silver in the newly formed alloy is **9:11**.

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