'A' and 'B' alone can complete a work in 14 days and 21 days, respectively. Find the time taken by them to complete the work if they work on alternate days starting with 'B'.

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