A, B, and C are capable of completing a job in 30, 45, and 90 days, respectively. A works every day, while B and C join A every fifth day. How long will it take to finish the task?
25 days
Take total work = LCM(30, 45, 90) = 90 units.
Daily rates: A = \(90/30 = 3\), B = \(90/45 = 2\), C = \(90/90 = 1\) units/day.
On the 5th, 10th, 15th… days, all three work: \(3 + 2 + 1 = 6\) units that day.
On the other 4 days out of every 5, only A works: \(3\) units each.
Work per 5-day cycle = \(4 \times 3 + 1 \times 6 = 12 + 6 = 18\) units.
Number of 5-day cycles needed = \(\tfrac{90}{18} = 5\) full cycles.
Total days = \(5 \times 5 = 25\) days.
Hence, the task is completed in 25 days.
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