A and B working separately can do a piece of work in 9 and 15 days respectively. If they work for a day alternatively, with A beginning, then the work will be completed in ?

Answer: Option B

L.C.M. of Total Work = 45
One day work of A = $$\frac{45}{9}$$ = 5 unit/day
One day work of B = $$\frac{45}{15}$$ = 3 unit/day
$$\begin{array}{rl}& \left(\text{A}+\text{B}\right)\text{’s 2 days work }\\ & =5+3\\ & =8\text{ units}\\ & \text{They will do in }\\ & =\frac{40}{8}\times 2\\ & =\left(5\times 2\right)\\ & =10\text{ days}\\ & \therefore \text{Work left}\\ & =45-40\\ & =\text{5 units}\\ & \text{Now,}\\ & \text{A’s turn and he will complete in}\\ & =\frac{5}{5}\\ & =1\text{ days}\\ & \text{Then total work completed in}\\ & =10+1\\ & =11\text{ days}\end{array}$$