P, Q and R can complete a work alone in 12, 15 and 20 days respectively. They started the work together. P left the work 8 days before the work was completed and Q left the work 5 days after P had left. R completed the remaining work alone. How many days will be required to complete the whole work?

28/3 days

P = 12 days, Q = 15 days, R = 20 days,

According to the question,

⇒ R alone does the work in last 3 days = (3) x 3 = 9 units,       ..(Efficiency × Days = Work)

⇒ R + Q work 5 days (before Q leaving), therefore work done in 5 days = (4 + 3) x 5 = 35 units.

⇒ Remaining work done by (P + Q + R) (before P leaving),

⇒ Remaining work = 60 - (9 + 35) = 16 units,

⇒ Remaining work done by (P + Q + R) in = \(\frac{16}{12}\) = \(\frac{4}{3}\) days,

⇒ Total time = \(\frac{4}{3}\) + 5 + 3 = \(\frac{28}{3}\) days.