A, B and C can complete a piece of work in 10, 12 and 15 days respectively. A left the work 5 days before the work was completed and B left 2 days after A had left. Number of days required to complete the whole work was ?

Solution(By Examveda Team)

L.C.M. of total work = 60
One day work of A = $$\frac{{60}}{{10}}$$ = 6 unit/day
One day work of B = $$\frac{{60}}{{12}}$$ = 5 unit/day
One day work of C = $$\frac{{60}}{{15}}$$ = 4 unit/day
$$\eqalign{ & {\text{A leaves before 5 days}} \cr & = 6 \times 5 \cr & = 30 \cr & {\text{B leaves before 3 days}} \cr & = 3 \times 5 \cr & = 15 \cr & {\text{Then total work}} \cr & = 60 + 30 + 15 \cr & = 105 \cr & {\text{Total efficiency}} \cr & = 6 + 5 + 4 \cr & = 15 \cr & {\text{Total days requierd}} \cr & = \frac{{105}}{{15}} \cr & = 7{\text{ days}} \cr} $$