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.