IIM Bangalore (UGAT) (QA) PYQs

A can complete a piece of work alone in 120 hours, B can complete it alone in 180 hours, while C can complete it alone in 216 hours. In every cycle of three days, only A works on Day 1, only B works on Day 2, and only C works on Day 3. In the $n^{th}$ cycle, each of A, B, and C work for $n$ hours. An exception is made on the last day, if the work is completed mid cycle. What is the total number of days needed for the work to be completed? (Note: if on the final day of work, the person working is supposed to work for p hours, but the work gets over after just q hours, that should be considered as only $\frac{q}{p}$ day.)