At a university, the faculty-to-student ratio is 1:9, if two-thirds of the students are female and one-quarter of the faculty is female, what is the fraction of the female students and faculty out of total students and faculty?

It is given that faculty to student ratio = 1:9

Let the number of faculty be 100a, so students will be 900a

=> Two-thirds of students are female = $$\ \dfrac{2}{3}\times900$$a = 600a

=> Therefore, male students = 300a

Also, one-quarter of the faculty is female = $$\ \dfrac{1}{4}\times100$$a = 25a

Therefore, male faculty = 75a

The ratio of female students and faculty out of the total students and faculty = $$\dfrac{\left(600a+25a\right)\ }{1000a}$$

=> ratio = $$\ \dfrac{5}{8}$$

The answer is option D.