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 ?

Answer: Option A

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)
$$\begin{array}{rl}& \text{Work left }\Rightarrow 36-35=1\text{unit}\text{.}\\ & \text{Now, A’s turn}\text{.}\\ & \text{A completes}\\ & \Rightarrow \frac{1\text{ unit}}{\text{3 units/day}}\\ & =\frac{1}{3}\text{ day}\\ & \text{Whole work completes in}\\ & \Rightarrow 14+\frac{1}{3}\\ & =14\frac{1}{3}\text{ days}\end{array}$$