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

Let the total work to be done = 120 units

Rate at which A finishes work alone = $$\frac{120}{24}$$ = 5 units/day

Rate at which B finishes work alone = $$\frac{120}{30}$$ = 4 units/day

Rate at which C finishes work alone = $$\frac{120}{40}$$ = 3 units/day

Now, C left 4 days before completion of work, which means for the last 4 days, only A & B worked together

=> Amount of work done in last 4 days by A & B together = (5+4) * 4 = 36 units

Now, work left = 120-36 = 84 units

For the remaining days, all of them worked together

=> Time taken to finish 84 units of work by A, B & C together = $$\frac{84}{5+4+3}$$ = 7 days

Thus, total time taken = 7+4 = 11 days