If some persons can do a piece of work in 80 days. In how many days two times the number of such persons will do the half of that work?

20 days.

f the persons can do the work in 80 days, means the work requires the input of 80 man-days. If 2 such mens are engaged they will do the same work in 80 man-days/2 men = 40 days. If half the work needs to be completed it will be done in 40/2 = 20 days.