Explanation:

- A and B each can complete the work in 30 days alone, so together they do $\frac{1}{30}+\frac{1}{30}=\frac{1}{15}$ of the work per day without taking holidays.

- A works 4 days, rests 1 day. So, in 5 days, A works 4 days.

- B works 5 days, rests 1 day. So, in 6 days, B works 5 days.

- Together, A and B work 9 out of every 6 days.

- Daily work completed by both = $\frac{4}{30}+\frac{5}{30}=\frac{9}{30}=\frac{3}{10}$.

- In 5 cycles of 6 days (30 days total), together they would have completed $\frac{3}{10}\times 30=9$ or 90% of the work.

- On the 31st day, they need only 10%. A works; B works.

- Completing the remaining 10% requires $\frac{1}{3}$ of a day. This means it finishes on the 31st day, which is 18 August 2022.

- Option 4: 18 August 2022