brazen can paint a wall red in 12 hours while Ballari can paint The entire wall in 21 hours if brazen and ballari work alternately for an hour each from The time The wall is painted to red then how many hour will it take to paint The entire wall red

15 hrs.

Let the Area of the wall to be painted be LCM of 21 and 12 which is 84.
SO total area to be paint is 84.
Now Brazen can paint it in 12 hours its means in 1 hour Brazen will paint 84/12=7 sq unit of the wall.
Similarly Ballari will paint 84/21=4 sq unit of the area in 1 hour.
Now total area is 84.
Now if Brazen starts first .Then it will take 84/(7+4) hours + some hrs
for first 14 hrs they will paint 11*7=77 sq unit and then in 1 more hour brazen will paint the remaining 7 unit.
So total required time=15 hours