A alone can complete 60% of a work in 36 days while B takes 30 days more than A to complete it. If B and C together can complete the work in 40 days, then find the time taken by C alone to complete the same work.

A's work rate: A completes 60% of the work in 36 days. A completes the full work in  36/0.6= 60 days. A's daily work rate is 1/60 B's work rate: B takes 30 days more than A, so B completes the work in 60+30 = 90 days. B's daily work rate is 1/90 . Combined work rate of B and C: B and C together complete the work in 40 days. Their combined daily work rate is 1/40. Find C's work rate: Let C's daily work rate be 1/C Combined rate equation:  1/90+1/C=1/40 Solve for 1/C :  Time taken by C alone: C completes the work in 72 days. Therefore, C alone takes 72days to complete the work.