Explanation:

8 hours 

Given: 

Time taken by 1st tap to fill the tank = 3 hours

Time taken by 2nd tap to fill the tank = 4 hours 

Concept used: 

Total capacity = LCM

Efficiency = Total capacity / Time 

Efficiency of outlet pipe always be negative 

Calculations: 

Total capacity = LCM (3, 4) = 12 

Efficiency of 1st tap = 12/3 = 4 

Efficiency of 2nd tap = 12/4 = 3

1/3 rd part of the tank = 12 x 1/3 = 4 

Remaining part of the tank = 12 - 4 = 8 

Total efficiency of both the tap = 4 - 3 = 1

Time takeb by both the taps to fill the remianing part of the tank = 8/1 = 8

Thus, the time taken to fill the tanks will be 8 hours.