P can complete a work in 15 days and Q in 24 days. They began the work together, but Q left the work 2 days before its completion. In how many days, was the work completed?

Let the total work to be done = L.C.M.(15,24) = 120 units

P can complete the work in 15 days, => P's efficiency = $$\frac{120}{15}=8$$ units/day

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

Let the work is completed in $$t$$ days, thus P worked for $$t$$ days while Q for $$(t-2)$$ days

=> $$8(t)+5(t-2)=120$$

=> $$8t+5t-10=120$$

=> $$13t=120+10=130$$

=> $$t=\frac{130}{13}=10$$

$$\therefore$$ The work is completed in 10 days.

=> Ans - (B)