Find a fraction which shall bear the same ratio to 1/27 that 3/5 does to 3/40.

Options

A. 5/27
B. 13/27
C. 8/27
D. can't be determined

Answer

To solve the problem, we need to find a fraction \( \frac{x}{y} \) that has the same ratio to \( \frac{1}{27} \) as \( \frac{3}{5} \) has to \( \frac{3}{40} \).

### Step-by-Step Solution:

1. **Set Up the Ratios**:
We start with the equation that represents the problem:
\[ \frac{x}{y} : \frac{1}{27} = \frac{3}{5} : \frac{3}{40} \]

2. **Cross-Multiply to Form an Equation**:
From the ratio, we can write:
\[ \frac{x}{y} = \frac{3/5}{3/40} \]
To simplify this, we can cross-multiply:
\[ \frac{x}{y} = \frac{3}{5} \times \frac{40}{3} \]

3. **Simplify the Right Side**:
Notice that the \( 3 \) in the numerator and denominator cancels out:
\[ \frac{x}{y} = \frac{40}{5} \]
Now simplify \( \frac{40}{5} \):
\[ \frac{x}{y} = 8 \]

4. **Express as a Fraction**:
We can express this as:
\[ \frac{x}{y} = \frac{8}{1} \]

5. **Find the Fraction Relative to \( \frac{1}{27} \)**:
Now, we need to relate this back to \( \frac{1}{27} \):
\[ \frac{x}{y} = 8 \cdot \frac{1}{27} = \frac{8}{27} \]

Thus, the fraction that bears the same ratio to \( \frac{1}{27} \) as \( \frac{3}{5} \) does to \( \frac{3}{40} \) is:
\[ \frac{8}{27} \]

### Final Answer:
The required fraction is \( \frac{8}{27} \).