‘A’, ‘B’ and ‘C’ can complete a piece of work in 60 days, 120 days and 80 days respectively. ‘A’ and ‘B’ started the work together but ‘A’ left the work after 15 days. Now ‘C’ joined the work and then after 9 days ‘B’ is replaced by ‘A’. Find the time taken to complete the rest of the work by ‘A’ and ‘C’ together.

Let total amount of work = 240 units (LCM of 60, 120 and 80) Amount of work done by ‘A’ in one day = 240/60 = 4 units Amount of work done by ‘B’ in one day = 240/120 = 2 units Amount of work done by ‘C’ in one day = 240/80 = 3 units Amount of work done by ‘A’ and ‘B’ together in 15 days = 15 × 6 = 90 units Amount of work done by ‘B’ and ‘C’ together in 9 days = 9 × 5 = 45 units Remaining work = 240 – 90 – 45 = 105 units Time taken by ‘A’ and ‘C’ together to complete the remaining work = 105/7 = 15 days