A work can be completed by P and Q in 12 days, Q and R in 15 days, R and P in 20 days. In how many days P alone can complete the work ?

A work can be completed by P and Q in 12 days, Q and R in 15 days, R and P in 20 days. In how many days P alone can complete the work ?
[A]10 days
[B]20 days
[C]30 days
[D]60 days

30 days
(P + Q)’s 1 day’s work = \frac{1}{12}……….(I)
(Q + R)’s 1 day’s work = \frac{1}{15}…….….(II)
(R + P)’s 1 day’s work = \frac{1}{20}……….(III)
On adding,
2(P + Q + R)’s 1 day’s work = \frac{1}{12}+\frac{1}{15}+\frac{1}{20} = \frac{5+4+3}{60} = \frac{1}{5}
∴ (P + Q + R)’s 1 day’s work = \frac{1}{5\times 2} = \frac{1}{10}……….(IV)
∴ P’s 1 day’s work = \frac{1}{10}-\frac{1}{15} = \frac{3-2}{20} = \frac{1}{30}
∴ P alone will complete the work in 30 days.
Hence option [C] is correct answer.

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