How often is the cabin air replaced in A320?
Let's do some simplified arithmetic:

The packs airflow in an A320 is 1.2 kg/s per pack in HIGH setting, but let's take the normal setting 1 kg/s, thus 2 kg/s considering both packs
The cabin of an A320 is around 190 m^3
Let's assume the cabin altitude in cruise 8000 ft, i.e. the air density at 20°C is 0.897 kg/m^3
The total airmass of the cabin is then 190×0.897 = 170.43 kg
Assuming that the cabin pressure is constant in cruise (so all the air coming from packs is going out via the outflow valve), in 90 seconds we change the following mass of air: 2 kg/s * 90 s = 180 kg

So 170.43 ~= 180, then 90 seconds is a correct estimation.