Question 21

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?

Solution

P = 12 days

Q = 16 days

total work = LCM(12,16) = 48

efficiency = $$\frac{48}{12}$$ = 4

efficiency = $$\frac{48}{16}$$ = 3

as we know that

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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