A can do a piece of work in 36 days, B in 54 days and C in 72 days. All the three began the work together but A and B left 8 days and 12 days before the completion of the work respectively. How many days in all did C put in till the entire work was finished?

Let total time taken to complete the work = 'x' days

C work for 'x' days.

A left 8 days before the completion of the work. So, A works for 'x - 8' days

B left 12 days before the completion of the work. So, B works for 'x - 12' days

Now, 

$$\frac{x - 8}{36} + \frac{x - 12}{54} + \frac{x}{72} = 1$$

$$\frac{6(x - 8) + 4(x - 12) + 3x}{216} = 1$$

6x - 48 + 4x - 48 + 3x = 216

x = 24

Hence, C works for total 24 days.