The combined rate of A and B is (1/20) + (1/30) = 1/12 of the work per day. Over 10 days, they complete 10/12, leaving 2/12 or 1/6 of the work. The estimated time was 12 days, so B and C had 3 days left, but they took 4 days; however, evaluating C's time directly from the remaining 1/6 of the work completed in 4 days yields C's rate at 1/24. Wait, the problem states they took 1 day more than the total estimated time of 12 days, meaning B and C took 3 days to finish the remaining 1/6 of the work. Their combined rate is (1/6) / 3 = 1/18. Subtracting B's rate of 1/30 gives C's rate: (1/18) - (1/30) = (5 - 3) / 90 = 2/90 = 1/45. Therefore, C would take 45 days to complete the work independently.