A alone can complete a work in 16 days and B alone in 12

Solution

Assume total work = LCM(16,12) = 48units A’s 1 day work = 48/16 = 3units  B’s 1 day work = 48/12 = 4 units So if they work on alternate days, total work in 2 days = 3 + 4 = 7 units Hence Work in 2 days = 7 units -----(1) Multiplying equation (1) by 6, we will get, Work done in 12 days = 42 units Remaining work =48-42 = 6 unit Work in 13th day by A = 3 units   So total work done in 13 days = 42 + 3 = 45 units now remaining work = 3unit Now, in next day, B can do 4 units work but remaining work is only (48 - 45) = 3. Hence B will take ¾ day to complete the remainig work 3 unit total  days = 13+3/4                             So Total days  =  13  days