A and B can complete a piece of work in 12 and 18 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be completed in ?

$$\eqalign{ & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 2 days work}} \cr & = \left( {\frac{1}{{12}} + \frac{1}{{18}}} \right) \cr & = \frac{5}{{36}} \cr & {\text{Work done in 7 pairs of days}} \cr & = \left( {\frac{5}{{36}} \times 7} \right) \cr & = \frac{{35}}{{36}} \cr & {\text{Remaining work}} \cr & = \left( {1 - \frac{{35}}{{36}}} \right) \cr & = \frac{1}{{36}} \cr & {\text{On 15th day, it is A's turn}}{\text{.}} \cr & \frac{1}{{12}}{\text{ work is done by A in 1 day}}{\text{.}} \cr & \frac{1}{{36}}{\text{ work is done by A in}} \cr & = \left( {12 \times \frac{1}{{36}}} \right) \cr & = \frac{1}{3}{\text{ day}}{\text{.}} \cr & \therefore {\text{Total time taken}} = 14\frac{1}{3}{\text{ days}} \cr} $$