A and B together can do a job in 2 days; B and C can do it in 4 days; A and C in $${\text{2}}\frac{2}{5}$$ days. The number of days required for A to do the job alone is = ?

$$\eqalign{ & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} = \frac{1}{2} \cr & \left( {{\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} = \frac{1}{4} \cr & \left( {{\text{A}} + {\text{C}}} \right){\text{'s 1 day's work}} = \frac{5}{{12}} \cr & {\text{Adding, we get: }} \cr & {\text{2}}\left( {{\text{A}} + {\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{2} + \frac{1}{4} + \frac{1}{{12}}} \right) \cr & = \frac{{14}}{{12}} \cr & = \frac{7}{6} \cr & \Rightarrow \left( {{\text{A}} + {\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} = \frac{7}{{12}} \cr & {\text{So, A's 1 day's work}} \cr & = \left( {\frac{7}{{12}} - \frac{1}{4}} \right) \cr & = \frac{4}{{12}} \cr & = \frac{1}{3} \cr & \therefore {\text{A alone can do the work in 3 days}}{\text{.}} \cr} $$