Easiest way is to do the math.
Figure what your drive pulley diameter is on the motor, vs the driven on the gear box, take that ratio to get Rpm, factor the box 1:5 to 1, take that ratio/rpm then figure the small sprocket teeth vs the large sprocket on the auger & factor in that ratio/rpm and you will have the theoretical auger RPM.
It sounds way more complicated than it is.
As ppl change driven pulley diameters, gear boxes with different ratios. and small drive sprockets your rpm's can vary, or be varied.
Say for instance, your gear box needs an orthodontist,
it is a 2:1 ratio.
you can't get what you need quick, and it is still snowing.
You have a 1:5 to 1, setting on the shelf for your tiller.
No problem, mount it and change your small sprocket a few teeth on the
drive shaft of the thrower.
ya you might have to go to tsc and get a sprocket and do some drilling.
but easier than hand shoveling. BTDT