A can do a piece of work in 24 days, B in 32 days, and C in 64 days. They start together but A leaves after 6 days and B leaves 6 days before the completion of the work. Find the total number of days taken to complete the work.
Explanation:
Total work = LCM(24, 32, 64) = 192 units. Efficiency of A = 8, B = 6, C = 3. Let total days be x. A works for 6 days. B works for (x - 6) days. C works for x days. Total work = 6*8 + (x - 6)*6 + x*3 = 192 => 48 + 6x - 36 + 3x = 192 => 9x + 12 = 192 => 9x = 180 => x = 20 days.
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