In an amalgam, mercury and silver are in the ratio of 3 : 7. In the second amalgam, the ratio of same elements is 1 : 9. If equal quantities of these two amalgam are mixed to form a new amalgam, then what will be the ratio of both of these elements in the new amalgam?

Options

A. `1:4`
B. `7:81`
C. `4:15`
D. `2:7`

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the ratios in the two amalgams.
- In the first amalgam, the ratio of mercury to silver is 3:7.
- In the second amalgam, the ratio of mercury to silver is 1:9.

### Step 2: Define the total parts in each amalgam.
- For the first amalgam, the total parts = 3 (mercury) + 7 (silver) = 10 parts.
- For the second amalgam, the total parts = 1 (mercury) + 9 (silver) = 10 parts.

### Step 3: Assume equal quantities of each amalgam.
Let’s assume we take an equal quantity of each amalgam, denoted as \( x \).

### Step 4: Calculate the quantity of mercury and silver in the first amalgam.
- Quantity of mercury in the first amalgam = \( \frac{3}{10}x \)
- Quantity of silver in the first amalgam = \( \frac{7}{10}x \)

### Step 5: Calculate the quantity of mercury and silver in the second amalgam.
- Quantity of mercury in the second amalgam = \( \frac{1}{10}x \)
- Quantity of silver in the second amalgam = \( \frac{9}{10}x \)

### Step 6: Combine the quantities of mercury and silver from both amalgams.
- Total quantity of mercury in the new amalgam = \( \frac{3}{10}x + \frac{1}{10}x = \frac{4}{10}x = \frac{2}{5}x \)
- Total quantity of silver in the new amalgam = \( \frac{7}{10}x + \frac{9}{10}x = \frac{16}{10}x = \frac{8}{5}x \)

### Step 7: Find the ratio of mercury to silver in the new amalgam.
- The ratio of mercury to silver = \( \frac{\frac{2}{5}x}{\frac{8}{5}x} \)
- This simplifies to \( \frac{2}{8} = \frac{1}{4} \)

### Conclusion:
The ratio of mercury to silver in the new amalgam is \( 1:4 \).

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