Explanation:

- A can complete the work in 36 days, so A's one day work is 1/36 of the total work.

- B can finish the work in 45 days, meaning B's one day work is 1/45 of the total work.

- Together, A and B can complete \( \frac{1}{36} + \frac{1}{45} \) of the work in one day.

- Calculating: \( \frac{1}{36} + \frac{1}{45} = \frac{5}{180} + \frac{4}{180} = \frac{9}{180} = \frac{1}{20} \) of the work per day.

- Therefore, in 2 days, A and B together completed \( 2 \times \frac{1}{20} = \frac{1}{10} \) of the work.

- Remaining work = \( 1 - \frac{1}{10} = \frac{9}{10} \).

- B completes \( \frac{1}{45} \) of the work per day, so to finish \( \frac{9}{10} \), the days required are \( \frac{9}{10} \times 45 = 40.5 \).

- Correct Answer: Option 4: 40.5

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