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

Solution(By Examveda Team)

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