Efficiency Questions

A can complete a piece of work alone in $200\text{days}$, while B can complete the same piece of work alone in $100\text{days}$. In every three-day cycle, both A and B work on day 1, only A works on day 2, and only B works on day 3. This cycle continues till the work is completed. How many days in all does it take the duo to complete the work?

Arvind works $4$ times as fast as Suresh. If Suresh can complete a work in $20$ days independently, then find the number of days in which Arvind and Suresh can together finish the work.