Explanation:

- Work rates:

- P can complete the entire work in 18 days, so P’s work rate is 1/18 of the work per day.

- Q can complete the entire work in 36 days, so Q’s work rate is 1/36 of the work per day.

- Combined work rate:

- When P and Q work together, their combined work rate is the sum of their individual work rates:

$\frac{1}{18}+\frac{1}{36}=\frac{2}{36}+\frac{1}{36}=\frac{3}{36}=\frac{1}{12}$

- Together, they complete 1/12 of the work per day.

- Time to complete the work together:

- Since their combined work rate is 1/12 per day, they will take 12 days to complete the work together.

- Option analysis:

- Option 1, 24 days: Too long for their combined efficiency.

- Option 2, 12 days: Correct calculation.

- Option 3, 20 days: Incorrect; does not match the work rate.

- Option 4, 10 days: Too short for their combined work rate.

- Conclusion and Correct Answer:

- Option 2, 12 days is the correct answer, as P and Q together can complete the work in 12 days.