To do a certain work, A and B work on alternate days, with B beginning the work on the first day. A can finish the work alone in 48 days and B can finish the work alone in 32 days. How many days taken by A and B to finish the work?

38\(\frac{1}{3}\)

1^st day work (B) = 3

2^nd day work (A) = 2

2 days work = 5

↓                     ↓

38                 95

Remaining work = 96 - 95 = 1

Remaining work to be done by B in = \(\frac{1}{3}\) day

Total time = 38 + \(\frac{1}{3}\) = 38\(\frac{1}{3}\) days