'A' and 'B' alone can complete a work in 9 days and 18

Solution

ATQ, Let the total work be the LCM of 9 and 18, which is 18 units. Efficiency of 'A' = 18/9=2 units/day Efficiency of 'B' = 18/18=1 unit/day If the work was started by 'A', then on the first day, work completed by 'A' = 2 units On the next day, work completed by 'B' = 1 unit Therefore, in two days, the amount of work completed by 'A' and 'B' = 2 + 1 = 3 units So, in 12 days, work completed by 'A' and 'B' = 3 × 6 = 18 units Therefore, total time taken by them to complete the work = 12 days