A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?

One days work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10. C leaves 4 days before completion of the work, which means only A and B work during the last 4 days. Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10. Remaining Work = 7/10, which was done by A,B and C in the initial number of days. Number of days required for this initial work = 7 days. Thus, the total numbers of days required = 4 + 7 = 11 days.