Explanation:

- Let the distance be 'd' km.

- Time taken by A = $\frac{d}{8}$ hours.

- Time taken by B = $\frac{d}{12}$ hours.

- Given: B takes 30 minutes (or 0.5 hours) less than A.

- Equation:

$\frac{d}{8}-\frac{d}{12}=0.5$

- Solving the equation:

Multiply by 24 to clear fractions: $3d-2d=12$

So, $d=12$.

- Distance is 12 km.

- Option 1 is correct.

- Reasons for incorrect options:

- 10 km: Results in wrong time difference.

- 15 km: Yields a larger time difference.

- 8 km: Results in smaller time difference.

Answer: Option 1 - 12