A can lay railway track between two given stations in 16 days and B can do the s

Question

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:

Options:

A . \(9\frac{1}{5}days\)

B . \(9\frac{2}{5}days\)

C . \(9\frac{3}{5}days\)

D . 10

Answer: Option C

\(9\frac{1}{5}days\)(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 = \(\frac{1}{12}.\)

So, C's 1 day's work = \(\frac{1}{4}-\left(\frac{1}{16}+\frac{1}{12}\right)= \left(\frac{1}{4}-\frac{7}{48}\right)=\frac{5}{48}\)

So, C alone can do the work in \(\frac{48}{5}=9\frac{3}{5}days\)

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