'A' and 'B' alone can complete a work in 14 days and 21

Solution

ATQ, Let the total work be the LCM of 14 and 21, which is 42 units. Efficiency of 'A' = 42/14 =3 units/day Efficiency of 'B' = 42/21=2 units/day If the work was started by 'B', then on the first day, work completed by 'B' = 2 units On the next day, work completed by 'A' = 3 units Therefore, in two days, the amount of work completed by 'A' and 'B' = 2 + 3 = 5 units So, in 14 days, work completed by 'A' and 'B' = 5 × 7 = 35 units Remaining work = 42 - 35 = 7 units The remaining work will be completed by 'B' in 7/2=3.5 days Therefore, total time taken by them to complete the work = 14 + 3.5 = 17.5 days