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1. 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. 24 days

B. 25 days

C. 27 days

D. 30 days

Solution:

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,

\begin{aligned} \frac{x - 8}{36} + \frac{x - 12}{54} + \frac{x}{72} = 1 \\ \frac{6 x - 48 + 4 x - 48 + 3 x}{216} = 1 \\ 13 x - 96 = 216 \\ 13 x = 216 + 96 = 312 \\ x = \frac{312}{13} \\ x = 24 days \end{aligned}

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