Statement I: It is given that the first painter can paint the board in 12 hours. There is no information about the work efficiency of the second person. So the question cannot be answered.
Statement II: Here the information about only the second painter is given. So it is again not sufficient.
Now if we combine both the statements, the amount of work done by both the painters in 1 hour is
So the two painters will take 24/5 hours or 4 hours 48 minutes to complete the work. Since half the board is painted till 12 noon, so the work will be complete by 2: 24 pm.