Your calculation is for 20% nicotine, 60% PG, 20% VG.
For 10% nicotine, you'd have 90%*3/4 = 67.5% PG and 90%*1/4 = 22.5% VG. Too busy to figure it out, but I'm sure you guys can. I've no idea why you need to know the exact ml quantity in advance, though. If you are going to dilute it...