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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?

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? Correct Answer 24 days

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,
$$\eqalign{ & {\frac{{ {x - 8} }}{{36}} + \frac{{ {x - 12} }}{{54}} + \frac{x}{{72}}} = 1 \cr & {\frac{{ {6x - 48 + 4x - 48 + 3x} }}{{216}}} = 1 \cr & 13x - 96 = 216 \cr & 13x = 216 + 96 = 312 \cr & x = \frac{{312}}{{13}} \cr & x = 24\,{\text{days}} \cr} $$

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