Explanation:

We are given that A fills the pool at the rate of 4 liters every 3 minutes and B fills the pool at the rate of 3 liters every 4 minutes.
=> Pool filled by A in 12 minutes = 4 x 4 = 16 liters
=> Pool filled by B in 12 minutes = 3 x 3 = 9 liters
=> Pool filled in 12 minutes = 16 + 9 = 25 liters
or we can say to fill 25 liters water, they will take 12 minutes.
Therefore to fill 1000 liters they will take (12*1000)/25 minutes i.e. 8 hours.
=> Since they will put a bucket at the same instant every 12 minutes. (LCM of 3 and 4 minutes = 12 minutes).
=> After every 12 minutes they will take rest for 3 minutes.
=> Overall  (8*60)/12 i.e 40 times they take rest while working .
=> So every 12 minutes should be considered 15 (12+3) minutes for 40 times.
=> But after having taken 39 times . The pool of capacity 1000 liters will be filled.
=> Last 3 minutes must not be considered.
Therefore, to fill 1000 liters (25 x 40 liters), it would take (12*1000)/25 minutes i.e. 8 hours. + (39*3) minutes = 8 hrs. + 117 minutes
So ans is  9 hrs 57 minutes.