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

Answer

To solve the problem of finding the ratio of gold and silver in the newly formed alloy from Alloy A and Alloy B, we can follow these steps:

### Step 1: Determine the weights of Alloys A and B
Assume the weight of Alloy A is 100 kg. Since the alloys are mixed in the ratio of 1:4, the weight of Alloy B will be:
\[ \text{Weight of Alloy B} = 4 \times 100 \text{ kg} = 400 \text{ kg} \]

### Step 2: Calculate the amount of gold and silver in Alloy A
Alloy A contains:
- 40% gold
- 60% silver

Calculating the amounts:
- Gold in Alloy A:
\[ \text{Gold in A} = 40\% \text{ of } 100 \text{ kg} = \frac{40}{100} \times 100 = 40 \text{ kg} \]
- Silver in Alloy A:
\[ \text{Silver in A} = 60\% \text{ of } 100 \text{ kg} = \frac{60}{100} \times 100 = 60 \text{ kg} \]

### Step 3: Calculate the amount of gold and silver in Alloy B
Alloy B contains:
- 35% gold
- 40% silver
- 25% copper

Calculating the amounts for Alloy B (400 kg):
- Gold in Alloy B:
\[ \text{Gold in B} = 35\% \text{ of } 400 \text{ kg} = \frac{35}{100} \times 400 = 140 \text{ kg} \]
- Silver in Alloy B:
\[ \text{Silver in B} = 40\% \text{ of } 400 \text{ kg} = \frac{40}{100} \times 400 = 160 \text{ kg} \]

### Step 4: Calculate the total amounts of gold and silver in the new alloy
Now, we can find the total amounts of gold and silver in the newly formed alloy:
- Total gold:
\[ \text{Total Gold} = \text{Gold in A} + \text{Gold in B} = 40 \text{ kg} + 140 \text{ kg} = 180 \text{ kg} \]
- Total silver:
\[ \text{Total Silver} = \text{Silver in A} + \text{Silver in B} = 60 \text{ kg} + 160 \text{ kg} = 220 \text{ kg} \]

### Step 5: Find the ratio of gold to silver
Now, we can find the ratio of gold to silver in the newly formed alloy:
\[ \text{Ratio of Gold to Silver} = \frac{\text{Total Gold}}{\text{Total Silver}} = \frac{180 \text{ kg}}{220 \text{ kg}} \]

To simplify this ratio:
\[ \frac{180}{220} = \frac{18}{22} = \frac{9}{11} \]

### Final Answer
The ratio of gold to silver in the newly formed alloy is:
\[ \text{Ratio of Gold to Silver} = 9:11 \]

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