A, B, and C each have different rates of completing a task; A can finish it in 36 days, B in 60 days, and C in 30 days. Initially, they begin the work collaboratively, but C departs after 5 days. Furthermore, A exits the job 18 days before the final completion. How long does it take to complete the entire task?

Let the total work = 180 units (LCM of 36, 60 and 30) Amount of work done by A alone in one day = 180/36 = 5 units Amount of work done by B alone in one day = 180/60 = 3 units Amount of work done by C alone in one day = 180/30 = 6 units Amount of work done by A, B and C together in 5 days = 5 × (5 + 3 + 6) = 70 units Amount of work done by B alone in 18 days = 18 × 3 = 54 units Remaining work = 180 – 70 – 54 = 56 units Time taken by A and B together to complete 56 units work = 56/(5 + 3) = 7 days So the total time taken to complete the work = 5 + 18 + 7 = 30 days