To solve this problem, let's consider the fraction as \(\frac{x}{y}\). We are given two conditions:

1. When 1 is subtracted from the numerator, the fraction becomes \(\frac{1}{3}\). This gives us the equation: \(\frac{x-1}{y} = \frac{1}{3}\).
2. When 8 is added to the denominator, the fraction becomes \(\frac{1}{4}\). This gives us the equation: \(\frac{x}{y+8} = \frac{1}{4}\).

Let's solve these equations step by step:

Step 1: Solve the first equation

The first equation is \(\frac{x-1}{y} = \frac{1}{3}\). By cross-multiplying, we get:

\(3(x - 1) = y\)

Which simplifies to:

\(3x - 3 = y \quad \Rightarrow \quad y = 3x - 3\)

Step 2: Solve the second equation

The second equation is \(\frac{x}{y+8} = \frac{1}{4}\). By cross-multiplying, we get:

\(4x = y + 8\)

Step 3: Substitute for \(y\)

From step 1, we know that \(y = 3x - 3\). Substitute this expression for \(y\) in the second equation:

\(4x = (3x - 3) + 8\)

This simplifies to:

\(4x = 3x + 5\)

Subtract \(3x\) from both sides:

\(x = 5\)

Step 4: Solve for \(y\) using \(x = 5\)

Substitute \(x = 5\) into \(y = 3x - 3\):

\(y = 3 \times 5 - 3 = 15 - 3 = 12\)

So, the original fraction is \(\frac{x}{y} = \frac{5}{12}\).

Conclusion

The correct answer is \(\frac{5}{12}\). This matches the first option given.