A and B alone can complete work in 9 days and 18 days respectively. They worked together however 3 days before the completion of the work A left . In how many days was the work completed?

Let total work be 1 unit. A's rate is 1/9 per day and B's rate is 1/18 per day. Together their rate is 1/9 + 1/18 = 1/6 per day. Since A left 3 days before completion, B worked alone for those 3 days and completed 3/18 = 1/6 of the work. The remaining 5/6 was done together in (5/6) / (1/6) = 5 days. Total time = 5 + 3 = 8 days.