A can complete $$\frac{2}{3}$$ of a work in 8 days. B can complete $$\frac{3}{5}$$ of the same work in 12 days and C can complete $$\frac{4}{9}$$ of the same work in 8 days. A and B worked together for 5 days. How much time(in days) will C alone take to complete the remaining work?

Let total work to be done be L.C.M.(3,5,9) = 45 units

Thus, A complete $$\frac{2}{3}$$ of the work in 8 days, => 30 units in 8 days

=> A's efficiency = $$\frac{30}{8}=3.75$$ units/day

Similarly, B's efficiency = $$\frac{27}{12}=2.25$$ units/day

and C's efficiency = $$\frac{20}{8}=2.5$$ units/day

Now, work done by A and B in 5 days = $$(3.75+2.25)\times5=30$$ units

$$\therefore$$ Remaining work done by C in = $$\frac{(45-30)}{2.5}=6$$ days

=> Ans - (A)