A and B can complete a work in 12 days and 18 days, respectively. A begins to do the work and they work alternately one at a time for 1 days each. The whole work will be completed in how many days?

(A + B)'s 2 day's work = (1/12) + (1/18) = 5/36
(A + B)'s 14 day's work = (5/36) x 7 = 35/36
Remaining work = 1 - (35/36) = 1/36
Now, it is the turn of A .
A's 1 day's work = 1/12
∴ 1/36 work is done by A in 12 x (1/36) days = 1/3 days
∴ Total time taken = 14¹/₃ days