Find the number which bears the same ratio to `(7)/(33)` that `(8)/(21)` does to `(4)/(9)`.

Answer

To solve the problem, we need to find a number \( \frac{x}{y} \) that has the same ratio to \( \frac{7}{33} \) as \( \frac{8}{21} \) does to \( \frac{4}{9} \).

### Step-by-Step Solution:

1. **Set Up the Ratios**:
We need to establish the relationship between the ratios. We can express this as:
\[ \frac{x}{y} : \frac{7}{33} = \frac{8}{21} : \frac{4}{9} \]

2. **Calculate the Ratio of \( \frac{8}{21} \) to \( \frac{4}{9} \)**:
To find this ratio, we divide \( \frac{8}{21} \) by \( \frac{4}{9} \):
\[ \frac{8}{21} \div \frac{4}{9} = \frac{8}{21} \times \frac{9}{4} \]
Simplifying this gives:
\[ = \frac{8 \times 9}{21 \times 4} = \frac{72}{84} \]
Now, we can simplify \( \frac{72}{84} \):
\[ = \frac{72 \div 12}{84 \div 12} = \frac{6}{7} \]

3. **Set Up the Equation**:
Now we have the ratio:
\[ \frac{x}{y} : \frac{7}{33} = \frac{6}{7} \]
This can be expressed as:
\[ \frac{x/y}{7/33} = \frac{6}{7} \]

4. **Cross-Multiply to Solve for \( \frac{x}{y} \)**:
Cross-multiplying gives us:
\[ 7 \cdot \frac{x}{y} = 6 \cdot \frac{7}{33} \]
Simplifying the right side:
\[ 7 \cdot \frac{x}{y} = \frac{42}{33} \]

5. **Isolate \( \frac{x}{y} \)**:
Now, divide both sides by 7:
\[ \frac{x}{y} = \frac{42}{33} \cdot \frac{1}{7} = \frac{42}{231} \]

6. **Simplify \( \frac{42}{231} \)**:
We can simplify this fraction:
\[ = \frac{42 \div 21}{231 \div 21} = \frac{2}{11} \]

7. **Conclusion**:
Therefore, the number that bears the same ratio to \( \frac{7}{33} \) as \( \frac{8}{21} \) does to \( \frac{4}{9} \) is:
\[ \frac{x}{y} = \frac{2}{11} \]

### Final Answer:
The required number is \( \frac{2}{11} \).