Question

if p and q can complete a work in 20 days ; q and r can complete a work in 10 days ; r and p can complete a work in 15 days find how much time will p q r take to complete the work individually??????

Answer 1

(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.