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1. A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:

A. $9 \frac{1}{5}$ days

B. $9 \frac{2}{7}$ days

C. $9 \frac{3}{5}$ days

D. 10

Solution:

\begin{aligned} (A + B + C)'s 1 day's work = \frac{1}{4} \\ A's 1 day's work = \frac{1}{16} \\ B's 1 day's work = \frac{1}{12} \\ ∴ C's 1 day's work \\ = \frac{1}{4} - (\frac{1}{16} + \frac{1}{12}) = \frac{1}{4} - \frac{7}{48} = \frac{5}{48} \\ So, C alone can do the work in \\ \frac{48}{5} = 9 \frac{3}{5} days \end{aligned}

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