Explanation:

Let's solve the problem step-by-step:

- Let's denote the original fraction as $\frac{x}{y}$.

- Statement 1: When 8 is added to the numerator and 12 to the denominator, the fraction becomes $\frac{1}{2}$.

- This gives us the equation: $\frac{x+8}{y+12}=\frac{1}{2}$.

- Cross multiply: $2(x+8)=y+12$.

- Statement 2: When 2 is subtracted from both the numerator and the denominator, the fraction becomes $\frac{1}{8}$.

- This gives the equation: $\frac{x-2}{y-2}=\frac{1}{8}$.

- Cross multiply: $8(x-2)=y-2$.

- Solve the system of equations:

- From $2(x+8)=y+12$, we get $y=2x+4$.

- From $8(x-2)=y-2$, we get $y=8x-14$.

- Equate the expressions for $y$:

- $2x+4=8x-14$.

- Solving this, $6x=18$ or $x=3$.

- Substitute $x=3$ in $y=2x+4$: $y=10$.

- Original fraction is $\frac{3}{10}$.

- Option 2, $3/10$, is the correct answer.

- Correct Answer: Option 2, $\frac{\mathbf{3}}{\mathbf{10}}$