'A' and 'B' together can complete 60% of a work in 30 days while 'B' and 'C' together can complete 80% of the same work in 30 days. If 'A', 'B' and 'C' worked on it for 15 days, 30 days and 30 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 = 30/0.60 = 50 days Time taken by 'B' and 'C' together to complete the whole work = 30/0.80 = 37.5 days Let total work = 750 units {LCM of 50 and 37.5} Combined efficiency of 'A' and 'B' = 750/50 = 15 units per day Combined efficiency of 'B' and 'C' together = 750/37.5 = 20 units per day Amount of work completed by 'A' and 'B' together in 15 days = 15 X 15 = 225 units Amount of work completed by 'B' and 'C' together in 15 days = 15 X 20 = 300 units Remaining work = 750 - 225 - 300 = 225 units So, 225 units of work is completed by 'C' in 15 days So, efficiency of 'C' = 225/15 = 15 units per day Efficiency of 'B' = 20 - 15 = 5 units per day Efficiency of 'A' = 15 - 5 = 10 units per day Required time = 750/10 = 75 days