The labourers A, B, C were given a contract of Rs. 750 for doing a certain piece of work. All the three together can finish the work in 8 days, A and C together can do it 12 days, while A and B together can do it in $${\text{13}}\frac{1}{3}$$ days. The money will be divided in the ratio ?

Solution(By Examveda Team)

L.C.M. of Total Work = 120
One day work of A + B + C = $$\frac{{120}}{{8}}$$ = 15 unit/day
One day work of A + B = $$\frac{{120}}{{\frac{{40}}{3}}}$$ = 9 unit/day
One day work of A + C = $$\frac{{120}}{{12}}$$ = 10 unit/day
$$\eqalign{ & {\text{C's efficiency}} = 15 - 9 = 6 \cr & {\text{B's efficiency}} = 15 - 10 = 5 \cr & {\text{A's efficiency}} = 15 - \left( {6 + 5} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15 - 11 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4 \cr & {\text{So, A}}:{\text{B}}:{\text{C}} = 4:5:6 \cr} $$