A does one-third of a work in a week. B finishes the same in a fortnight. B starts the working and works only for 12 days. A will finish the remaining work in ?

3 days

A does one-third of a work in a week

Therefore, A complete the work in 7 x 3 i.e. 21 days 

B completes the same work in fortnight i.e. 14 days 

Work completed by B in 12 days = efficiency x days = 3 x 12 = 36

Work left = 42 - 36 = 6

Time taken by A to complete the remaining work = \(\frac{work\; left}{Efficiency}\)

                                                                       = \(\frac{6}{2}\) = 3 days