P and Q can do a work in 12 days and 16 days respectively. P started the work alone. After how many days should Q join P, so that the work is finished in 9 days?
P = 12 days
Q = 16 days
total work = LCM(12,16) = 48Â
efficiency = $$\frac{48}{12}$$ = 4
efficiency = $$\frac{48}{16}$$ = 3
as we know thatÂ
efficiency multiplayed by days = work
P works till the end and Q comes after some day
so
$$Ptime\times P effi + Qtime\times Qeffi = 48$$
$$9\times 4+ Q\times 3$$ = 48
Q time = 4 days
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