Ajay starts painting hiz room for sometime between 6 and 7 o'clock in the evening. when he finished painting the room per sometime between 8 and 9 o'clock in the evening and he notices that the hours and minutes hand have interchanged their positions with what they were when he started painting. at what time did the paint job get over?

Let the time when he started be 6 hours x mins and the time when he ended be 8 hours y mins.
Starting time: HR HAND covers an angle of 30(6 + x/60), MIN HAND covers an angle of 6x
End time: HR HAND covers an angle of 30(8 + y/60), MIN HAND covers 6y
Equating them we get,
30(6 + x/60) = 6y and 30(8 + y/60) = 6x
Solving, we will get the value of y close to 33.56 mins

8:33.55 approx

8:34