Two teachers, A and B, can complete an academic work in 10 days and 15 days respectively. They started the work together, but A left after 5 days and another teacher C joined, who alone can complete the work in 60 days. In how many days did the work get completed?

Let the total work be the least common multiple of 10, 15, and 60, which is 60 units. The daily work capacities are A at 6 units, B at 4 units, and C at 1 unit. Working together for 5 days, A and B complete (6 + 4) * 5 = 50 units of work. The remaining work is 60 minus 50, which is 10 units. B and C then work together at a rate of 4 + 1 = 5 units per day, taking 10 divided by 5, which equals 2 days. The total time to complete the work is 5 days plus 2 days, resulting in 7 days.

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