Well you know that the amount of boys that voted for Danny has to be 123 - 55, so you do that and get 68, then the ratio of girls to boys is 55:68, and that can't be simplified anymore because 55 has factors of only 1, 55, 11, and 5, and that doesn't get you anywhere.
The answer is 62/95. You determine this by calculating the probability of both students being girls.
Probability first student is girl: 12/20 Probability second student is girl: 11/19 Multiply 12/20 * 11/19 = 132/380 or 0.347 Probability of both students not being girls: 1 - 0.347 = 0.653 or 62/95