'A' and 'B' together can complete 50% of a work in 40 days while 'B' and 'C' together can complete 75% of the same work in 40 days. If 'A', 'B' and 'C' worked on it for 20 days, 40 days and 40 days, respectively and completed the whole work, then find time taken by 'A' alone to complete the whole work.

Time taken by 'A' and 'B' together to complete the whole work = 40/0.50 = 80 days Time taken by 'B' and 'C' together to complete the whole work = 40/0.75 = 160/3 days Let total work = 480 units {LCM of 80 and 160} Combined efficiency of 'A' and 'B' = 480/80 = 6 units per day Combined efficiency of 'B' and 'C' together = 480/160 X 3 = 9 units per day Amount of work completed by 'A' and 'B' together in 20 days = 20 X 6 = 120 units Amount of work completed by 'B' and 'C' together in 20 days = 20 X 9 = 180 units Remaining work = 480 - 120 - 180 = 180 units So, 180 units of work is completed by 'C' in 20 days So, efficiency of 'C' = 180/20 = 9 units per day Efficiency of 'B' = 9 - 9 = 0 units per day Efficiency of 'A' = 6 - 0 = 6 units per day Required time = 480/6 = 80 days