A alone can complete a piece of work in 15 days, and B alone can complete it in 20 days. They work together, but every third day B does not work. In how many days will the whole work be completed?

Solution

A’s rate = 1/15 per day. B’s rate = 1/20 per day. Together = 1/15 + 1/20 = 7/60 per day. Work pattern over 3 days: Day 1: A + B → 7/60 Day 2: A + B → 7/60 Day 3: A only → 1/15 = 4/60 Total in 3 days = (7 + 7 + 4)/60 = 18/60 = 3/10. Total work = 1. Number of full 3-day cycles needed for most of the work: After 3 cycles (9 days), work done = 3 × (3/10) = 9/10. Work remaining = 1 − 9/10 = 1/10. On the 10th day, both A and B work: work done = 7/60 per day. Fraction of the 10th day needed: (1/10) / (7/60) = (1/10) × (60/7) = 6/7 day. Total time = 9 + 6/7 days = 9 (6/7) days.