A can do a piece of work in 30 days. A and B started doing the work, but midway through it, A fell sick and was absent from work for 3 days. Due to this, they took one more day to complete the work than the scheduled time. In how many days can B alone complete the piece of work?

Let B's rate be 1/x. A's rate = 1/30. Scheduled time T = 1 / (1/30 + 1/x) = 30x / (x+30). Actual time = T+1. Work done: (A+B) worked for (T+1)/2 - 1.5 days, then B worked alone for 3 days, then (A+B) finished. This is complex. Let's use: (A+B) worked for T+1 days total, but A was absent for 3 days. So A worked for (T+1) - 3 = T-2 days. B worked for T+1 days. (T-2)/30 + (T+1)/x = 1. Substitute T = 30x/(x+30). Solving this leads to x=15.