A, B and C alone can complete a work in 18, 32 and 24 days respectively. All of them started working together but after 3 days from start A left the job and after 5 more days B also left the job. So for how many days did C work?

Let the total work = 288 units (LCM of 18, 32 and 24) Amount of work done by A alone in one day = 288/18 = 16 units Amount of work done by B alone in one day = 288/32 = 9 units Amount of work done by C alone in one day = 288/24 = 12 units Amount of work done by A, B and C together in 3 days = 3 × (16 + 9 + 12) = 111 units Amount of work done by B and C together in 5 days = 5 × (9 + 12) = 105 units Remaining work = 288 – 111 – 105 = 72 units So, the time taken by C alone to complete 72 units work = 72/12 = 6 days So, C worked for 6 + 3 + 5 = 14 days