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

9 1/5 days
9 2/5 days
9 3/5 days
10 days

Correct answer: 9 3/5 days

Solution

A's rate is $\frac{1}{16}$ and B's rate is $\frac{1}{12}$. Together with C, they finish in 4 days, so combined rate is $\frac{1}{4}$; hence C's rate is $\frac{1}{4}-\frac{1}{16}-\frac{1}{12}=\frac{5}{48}$. Therefore, C alone takes $\frac{48}{5}=9\frac{3}{5}$ days.

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