The 240 is simply reverse-engineered from the assumption I mentioned above, so that we end up with 12 months for X=20.

Therefore, yes, if we talk about units of measurement, strictly speaking it must be 240 months and the 20 is unitless. If you prefer to express the 20 as 20%, it has to be 2.4 months / 20% = 12 months.

In the end, we only have one unit of measurement, and that is "months", which we omitted in the formula for matters of readability.

Sorry for the confusion!