A can do a piece of work in 20 days and B can do the same piece of work in 30 days. They start working together and work for 5 days and then both leave the work. C alone finishes the remaining work in 14 days. In how many days will C alone finish the whole work?

Let total work is L.C.M. (20,30) = 60 units

A alone can complete the work in 20 days, => A's efficiency = $$\frac{60}{20}=3$$ units/day

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

Now, (A+B)'s 5 day's work = $$(3+2)\times5=25$$ units

Work left = $$60-25=35$$ units

Now, 35 units of work is completed by C alone in 14 days.

=> C's efficiency = $$\frac{35}{14}=2.5$$ units/day

$$\therefore$$ Days required by C alone to complete the work = $$\frac{60}{2.5}=24$$ days

=> Ans - (A)