A and B, working together, can complete a work in d days. Working alone, A takes (8 + d) days and B takes (18 + d) days to complete the same work. A works for 4 days. The remaining work will be completed by B alone, in:

To find the time when A and B, working together = $$\sqrt{more days taken by A \times more days taken by B}$$

d = $$\sqr{8 \times 18}$$ = 12

Time taken by A to complete the work = (8 + d) = 8 + 12 = 20

Time taken by B to complete the work = (18 + d) = 18 + 12 = 30

Let the total work be 60.

(LCM of 20 and 30 is 60.)

Efficiency of A = 60/20 = 3

Efficiency of B = 60/30 = 2

Work done by A in 4 days = efficiency $$\times time = 3 \times 4 = 12$$

Remaining work = 60 - 12 = 48

Time taken by B to complete the remaining work = 48/2 = 24 days

$$\therefore$$ The remaining work will be completed by B alone, in 24 days.