As the pipes are operating alternatively, thus their 2 minutes job is =
In the next 2 minutes the pipes can fill another part of cistern.
Therefore, In 4 minutes the two pipes which are operating alternatively will fill Remaining part =
Pipe A can fill of the cistern in 1 minute
Pipe A can fill of the cistern in = min
Therefore, Total time taken to fill the Cistern
4 + minutes.