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