P alone can complete a work in 16 days and Q alone can complete the same work in 20 days. P and Q start the work together but Q leaves the work 7 days before the completion of work. In how many days the total work will be completed?
Let total work to be done = L.C.M.(16,20) = 80 units
=> P's efficiency = $$\frac{80}{16}=5$$ units/day and Q's efficiency = $$4$$ units/day
Let the work is finished in $$t$$ days, then P alone worked for 7 days, and P and Q together worked for $$(t-7)$$ days
According to ques,
=> $$9(t-7)+(5\times7)=80$$
=> $$9t-63+35=80$$
=> $$t=\frac{108}{9}=12$$ days
=> Ans - (C)
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