A and B together can do a piece of work in 8 days, B and C together in 10 days, while C and A together in 6 days, if they all work together the work will be completed in ?

Solution(By Examveda Team)

In these kind of questions, always take total work as L.C.M. of number of days
Here L.C.M. of Total Work = 120
One day work of A + B = $$\frac{{120}}{8}$$ = 15 unit/day
One day work of B + C = $$\frac{{120}}{10}$$ = 12 unit/day
One day work of C + A = $$\frac{{120}}{6}$$ = 20 unit/day
∴ Total units per day = 15 + 12 + 20 = 47
∴ Efficiency of :
$$\eqalign{ & 2\left( {{\text{A}} + {\text{B}} + {\text{C}}} \right) = 47 \cr & {\text{A}} + {\text{B}} + {\text{C}} = \frac{{47}}{2} \cr} $$
(A + B + C) will complete the whole work in
$$\eqalign{ & = \frac{{120}}{{\frac{{47}}{2}}} \cr & = \frac{{240}}{{47}} \cr & = 5\frac{5}{{47}}{\text{days}} \cr} $$