What is the difference between the total number of Associate Professors in universities J and M together and the total number of Professors in the same universities together?

Number of Associate Professors in university J = 75

Number of Associate Professors in university M = 21

=> Total associate professors in universities J and M = 75 + 21 = 96

Total number of assistant or associate professors in university J = $$\frac{60}{100} \times 250 + 75$$

= $$150 + 75 = 225$$

Thus, total professors in university J = $$250 - 225 = 25$$

Similarly, total number of assistant or associate professors in university M = $$\frac{63}{100} \times 100 + 21$$

= $$63 + 21 = 84$$

Thus, total professors in university M = $$100 - 84 = 16$$

=> Total number of Professors in the same universities together = 25 + 16 = 41

$$\therefore$$ Required difference = $$96 - 41 = 55$$