A, B and C can complete a work in 5, 12 and 30 days respectively. In how many days can A, B and C together can do $$\frac{4}{7}$$ of the same work?

Let work done = L.C.M.(5,12,30) = 60 units

A can complete the work in 5 days, => A's efficiency = $$\frac{60}{5}=12$$ units/day

B's efficiency = $$\frac{60}{12}=5$$ units/day

C's efficiency = $$\frac{60}{30}=2$$ units/day

=> (A+B+C)'s 1 day's work = $$(12+5+2)=19$$ units/day

$$\therefore$$ Time taken to finish $$\frac{4}{7}$$ of the same work = $$\frac{4}{7}\times60\times\frac{1}{19}$$

= $$\frac{240}{133}$$ days

=> Ans - (C)