A can complete a piece of work in 36 days, B in 54 days and C in 72 days. All the three began the work the work together but A left 8 days before the completion of the work and B 12 days before the completion of work. Only C worked up to the end. In how many days was the work completed?

Explanation:-

Let the work be completed in x days. C work for x days then A works for (x - 8) days and B works for (x - 12) days.
According to the question,
$$\eqalign{ & \left[ {\frac{{\left( {x - 8} \right)}}{{36}} + \frac{{\left( {x - 12} \right)}}{{54}} + \frac{x}{{72}}} \right] = 1 \cr & \left[ {\frac{{\left( {6x - 48 + 4x - 48 + 3x} \right)}}{{216}}} \right] = 1 \cr & 13x - 96 = 216 \cr & 13x = 216 + 96 = 312 \cr & x = \frac{{312}}{{12}} \cr & \,\,\,\,\, = 24\,{\text{days}} \cr}$$