You need a 1.5 : 1 ratio in addition to your 1 : 60 to have an overall ratio of 1 : 90 so you need 66.6666 teeth driving the 100 teeth. Obviously you are going to have to use 66 or 67 and cannot get exactly 1 : 90 unless you change the 100 teeth gear to something else.
I hope I did the calculation correct.
