A and B together can complete a work in 3 days. They started together but after 2 days B left the work. If the work is completed after 2 more days, B alone could do the work in how many days?

A and B together complete work in 3 days, so their combined rate is 1/3 work per day. After 2 days, they've completed 2/3 of the work. B leaves, and A completes the remaining 1/3 in 2 more days, so A's rate is (1/3)/2 = 1/6 per day alone. Since A + B = 1/3 and A = 1/6, then B = 1/3 - 1/6 = 1/6 per day. So B alone would take 6 days to complete the work.