P and Q can do a job in 3 days. Q and R can do the same job in 4 days, while R and P can do it in 12 days. In how many days the job will be finished when P, Q and R working together.

Question: P and Q can do a job in 3 days. Q and R can do the same job in 4 days, while R and P can do it in 12 days. In how many days the job will be finished when P, Q and R working together.

Solution:
Given that,
(P + Q)'s 1 day's work = 1/3
(Q + R )'s 1 day's work= 1/4
and
(R + P)'s 1 day's work = 1/12

Now, (P + Q) + (Q + R) + (R + P) = 2(P + Q + R)'s 1 day's work = (1/3) + (1/4) + (1/12)
= (4 + 3 + 1)/12
= 8/12 = 2/3
∴ (P + Q + R)'s 1 day's work = 2/(3 × 2) = 1/3

So, P + Q + R can complete the job in = 3 days