X, Y and Z can do a piece of work in 30, 40 and 50 days respectively. All three of them began the work together but Y left 4 days before completion of the work. In how many days was the work completed?

Let total work to be done = L.C.M. (30,40,50) = 600 units

X can do the work in 30 days, => X's efficiency = $$\frac{600}{30}=20$$ units/day

=> Y's efficiency = $$\frac{600}{40}=15$$ units/day

and Z's efficiency = $$\frac{600}{50}=12$$ units/day

Let work was completed in $$x$$ days, then X and Z work for $$x$$ days and Y for $$(x-4)$$ days

=> $$20x+15(x-4)+12x=600$$

=> $$32x+15x-60=600$$

=> $$47x=600+60=660$$

=> $$x=\frac{660}{47}$$

$$\therefore$$ Work was completed in 660/47 days.

=> Ans - (A)