A, B and C can do a piece of work in 10, 15 and 30 days respectively. In how many days can A do the work if he is replaced by B and C on every third day?

Let total work be LCM(10,15,30) = 30 units. A does 3 units/day, B does 2 units/day, C does 1 unit/day. In 3 days: day 1 (A) = 3 units, day 2 (A) = 3 units, day 3 (B+C) = 3 units. Total per 3 days = 9 units. For 30 units: 30/9 = 3.33 cycles of 3 days = 10 days. After 9 days, 27 units done, 3 remain. Day 10: A completes 3 units, finishing the work.