A B and C can do a piece of work in 20, 24 and 30 days respectively. All three of them began the work together but B left 3 days before completion of the work. In how many days was the work completed ?

Let total work to be done = L.C.M. (20,24,30) = 120 units

A can do it in 20 days, => A's efficiency = $$\frac{120}{20}=6$$ units/day

Similarly, B's efficiency = $$\frac{120}{24}=5$$ units/day

and C's efficiency = $$\frac{120}{30}=4$$ units/day

Let the work is completed in $$t$$ days, hence B worked for $$(t-3)$$ days and A and C worked for $$t$$ days.

According to ques,

=> $$6t+5(t-3)+4t=120$$

=> $$15t=120+15=135$$

=> $$t=\frac{135}{15}=9$$

$$\therefore$$ The work was completed in 9 days.

=> Ans - (D)