Question 327363
Let the amount of total work be 1.
The work done by the painter in one day = 1/4 of the total work.
The work done by the apprentice in one day = 1/6 of the total work. 
The work done by the two people together in one day = 1/4 + 1/6 = 5/12 of the total work.
1/6 of the total work is done by the apprentice alone for one day.
The remaining 5/6 of the total work is done by the painter and apprentice together for x days.
Therefore x = amount of work / work done in one day = (5/6)/(5/12) = 2 days.

Therefore, number of days taken to complete the work = 2 + 1 = 3 days.