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.