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?

Question: 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?

Solution:
One day's work of A, B, and C = (1/24) + (1/30) + (1/40) = 1/10.
C leaves four days before the work is completed, which means only A and B work during the last four days.
The work done by A and B together in the last four days is = 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.