P and Q together can do a piece of work in 30 days, Q and R together can do it in 20 days. P starts the work and works on it for 5 days, then Q takes it up and works for 15 days. Finally R finishes the work in 18 days. In how many days can R do the work when doing it separately?

Let P, Q, R be daily work rates. P+Q = 1/30, Q+R = 1/20. Work equation: 5P + 15Q + 18R = 1. Substitute P = 1/30 - Q and R = 1/20 - Q. This gives 5(1/30 - Q) + 15Q + 18(1/20 - Q) = 1. Solving: 1/6 - 5Q + 15Q + 9/10 - 18Q = 1, which simplifies to -8Q = -1/15, so Q = 1/120. Therefore R = 1/20 - 1/120 = 5/120 = 1/24. R alone takes 24 days.