The compound ratio of the inverse ratios of the ratios `x : yz, y : zx, z : xy` is :

Options

A. `1 : xyz`
B. `xyz : 1`
C. `1:1`
D. `x: yz`

Answer

To solve the problem, we need to find the compound ratio of the inverse ratios of the ratios \( x : yz, y : zx, z : xy \).

### Step-by-step Solution:

1. **Write the Ratios in Fraction Form**:
The given ratios can be expressed as:
\[ \frac{x}{yz}, \quad \frac{y}{zx}, \quad \frac{z}{xy} \]

2. **Find the Inverse of Each Ratio**:
To find the inverse of each ratio, we switch the numerator and denominator:
\[ \text{Inverse of } \frac{x}{yz} = \frac{yz}{x}, \quad \text{Inverse of } \frac{y}{zx} = \frac{zx}{y}, \quad \text{Inverse of } \frac{z}{xy} = \frac{xy}{z} \]

3. **Write the Inverse Ratios**:
Now we have the inverse ratios:
\[ \frac{yz}{x}, \quad \frac{zx}{y}, \quad \frac{xy}{z} \]

4. **Find the Compound Ratio**:
The compound ratio is found by multiplying the numerators together and the denominators together:
\[ \text{Numerator: } yz \cdot zx \cdot xy = y^2z^2x^2 \]
\[ \text{Denominator: } x \cdot y \cdot z = xyz \]

5. **Combine the Results**:
So, the compound ratio is:
\[ \frac{y^2z^2x^2}{xyz} \]

6. **Simplify the Compound Ratio**:
We can simplify this expression:
\[ = \frac{y^2z^2x^2}{xyz} = \frac{y^2z^2x^2}{xyz} = \frac{y^{2-1}z^{2-1}x^{2-1}}{1} = xyz \]

7. **Final Result**:
Thus, the compound ratio is:
\[ xyz : 1 \]

### Conclusion:
The final answer is \( xyz : 1 \).