A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in ?

A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in ? Correct Answer 8 days

L.C.M. of Total Work = 24
One day work of A + B = $$\frac{{24}}{{8}}$$ = 3 unit/day
One day work of B + C = $$\frac{{24}}{{12}}$$ = 2 unit/day
One day work of A + B + C = $$\frac{{24}}{{6}}$$ = 4 unit/day
$$\eqalign{ & {\text{Efficiency of C}} \cr & = 4 - 3 \cr & = 1 \cr & {\text{Efficiency of A}} \cr & = 4 - 2 \cr & = 2 \cr & {\text{Efficiency of B}} \cr & = 4 - 1 \cr & = 3 \cr & {\text{Efficiency of A}} + {\text{C}} \cr & = 2 + 1 \cr & = 1 \cr & {\text{Time taken by A}} + {\text{C}} \cr & = \frac{{24}}{3} \cr & = 8{\text{ days}} \cr} $$