A, B and C can complete a piece of work in 10, 12 and 15 days respectively. They started the work together, but A left after 2 days and B left 3 days before the completion of the work. Find the total duration of the work.
Explanation:
Total work = LCM(10, 12, 15) = 60 units. Efficiency of A = 6, B = 5, C = 4. Let the work last for x days. A works for 2 days: work = 12 units. B works for (x - 3) days: work = 5(x - 3). C works for x days: work = 4x. Total work = 12 + 5x - 15 + 4x = 60 => 9x - 3 = 60 => 9x = 63 => x = 7 days.
Explanation:
Total work = LCM(8, 12) = 24 units. Combined efficiency of A and B = 3. Efficiency of A = 2. Efficiency of B = 3 - 2 = 1. Time taken by B alone = 24 / 1 = 24 days.
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