Pipe A can fill an empty cistern in 4 hours while along with Pipe B it can fill it up in 3 hours. Only Pipe A is turned on for an hour after which Pipe is also turned on. How much total time will it take to fill up the cistern?

Let the capacity of the cistern be 12 units (LCM of 4 and 3)
Efficiency of Pipe A = 12/4 = 3 units/hour
Efficiency of Pipe A and B together = 12/3 = 4 units/hour
Then, Efficiency of Pipe B = 4-3 = 1 unit/hour
Given, that Pipe A is opened for 1 hour. Then, 3 units of cistern will be filled.
Remaining capacity is 9 units which should be filled by Pipes A and B together.
Remaining cistern will be filled in $$\dfrac{9}{4}$$ hours = 2 hours 15 minutes
Therefore, Total cistern will be filled in 2 hours 15 minutes + 1 hour = 3 hours 15 minutes