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:

1 $9 \frac{1}{5}$ $9\frac{1}{5}$ days
2 $9 \frac{2}{7}$ $9\frac{2}{7}$ days
3 $9 \frac{3}{5}$ $9\frac{3}{5}$ days
410

Answer:- 1

Explanation:-

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}

$\eqalign{ & \left( {{\text{A + B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{4} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{16}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{12}} \cr & \therefore {\text{C's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \frac{1}{4} - \left( {\frac{1}{{16}} + \frac{1}{{12}}} \right) = \left( {\frac{1}{4} - \frac{7}{{48}}} \right) = \frac{5}{{48}} \cr & {\text{So,}}\,{\text{C}}\,\,{\text{alone}}\,{\text{can}}\,{\text{do}}\,{\text{the}}\,{\text{work}}\,{\text{in}} \cr & \frac{{48}}{5} = 9\frac{3}{5}\,{\text{days}} \cr}$