Explanation:

- Let's understand the given problem:

- `p` men can complete the work in `q` days.

- With 50% more men, meaning `1.5p` men, the work finishes 12 days earlier than `q`.

- We can form equations to solve:

- Initial work equation: $p\times q=\text{Total Work}$

- With 50% more men: $1.5p\times (q-12)=\text{Total Work}$

- Equate both equations:

- $p\times q=1.5p\times (q-12)$

- Simplify: $q=1.5(q-12)$

- Solve for `q`: $q=1.5q-18\Rightarrow 18=0.5q\Rightarrow q=36$

- Correct and validated with calculations.

Option 3: 36 is the correct answer.