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 ?

Solution(By Examveda Team)

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
$$\eqalign{ & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 2 days work }} \cr & = 5 + 3 \cr & = 8{\text{ units}} \cr & {\text{They will do in }} \cr & = \frac{{40}}{8} \times 2 \cr & = \left( {5 \times 2} \right) \cr & = 10{\text{ days}} \cr & \therefore {\text{Work left}} \cr & = 45 - 40 \cr & = {\text{5 units}} \cr & {\text{Now,}} \cr & {\text{A's turn and he will complete in}} \cr & = \frac{5}{5} \cr & = 1{\text{ days}} \cr & {\text{Then total work completed in}} \cr & = 10 + 1 \cr & = 11{\text{ days}} \cr} $$