In college D, the respective ratio between the total number of male students and the total number of female students is 13 : 12. If the total number of female students in college E is three fourth of the total number of female students in college D. What is the respective ratio between total number of male students and total number of female students in college E?

Let the total number of students in all colleges together = $$100x$$

=> Number of students in A = $$\frac{25}{100} \times 100x = 25x$$

Number of students in C = $$\frac{60}{100} \times 25x = 15x$$

Number of students in college D = $$\frac{3}{4} \times 15x = \frac{45x}{4}$$

Number of students in E = $$\frac{1}{2} \times 15x = 7.5x = 450$$

=> $$x = \frac{450}{7.5} = 60$$

Ratio of male and female students in college D = 13 : 12

=> Female students in college D = $$\frac{12}{25} \times 675 = 324$$

=> Male students in college D = $$675 - 324 = 351$$

In college E, number of females = $$\frac{3}{4} \times 324 = 243$$

=> Male students in college E = $$450 - 243 = 207$$

$$\therefore$$ Required ratio = $$\frac{207}{243} = 23 : 27$$