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 complete in ?

A's one day work = 3 units
B's one day work = 2 units
A starts the work and does 3 units and B does the work 2 units/day.
They both do 5 units of work in 2 days.
They both do 35 units of work in 14 days
(Divide $${\frac{{36}}{5}}$$, take it to the closest)
$$\eqalign{ & {\text{Work left }} \Rightarrow 36 - 35 = 1{\text{unit}}{\text{.}} \cr & {\text{Now, A's turn}}{\text{.}} \cr & {\text{A completes}} \cr & \Rightarrow \frac{{1{\text{ unit}}}}{{{\text{3 units/day}}}} \cr & = \frac{1}{3}{\text{ day}} \cr & {\text{Whole work completes in}} \cr & \Rightarrow 14 + \frac{1}{3} \cr & = 14\frac{1}{3}{\text{ days}} \cr} $$