If the number of female Physics professors in the age group 25 - 34 equals 25% of all the Physics professors in that age group, then what is the number of male Physics professors in the age group 25 - 34?

To solve this problem, we need the total number of Physics professors in the age group 25-34. This value is implicitly provided in the context of the original UPSC question (e.g., from a preceding table or graph). Assuming the total number of Physics professors in the age group 25-34 is 12 (which is the value required to arrive at option A):

1. Calculate the number of female Physics professors: Female professors = 25% of Total professors Female professors = 0.25 * 12 = 3

2. Calculate the number of male Physics professors: Total professors = Female professors + Male professors 12 = 3 + Male professors Male professors = 12 - 3 = 9

Therefore, the number of male Physics professors in the age group 25-34 is 9.

Analyzing the options: A) 9: This is the correct answer, derived by assuming a total of 12 professors in the age group. B) 6: This would imply a total of 8 professors (25% of 8 = 2 female, 8-2 = 6 male). C) 3: This would imply a total of 4 professors (25% of 4 = 1 female, 4-1 = 3 male). D) 2: This would imply a total of 8/3 professors, which is not a whole number, or some other scenario not fitting the 25% rule cleanly for integer counts.

The explanation relies on the common UPSC practice where a total value is provided in an accompanying data set. For option A to be correct, the total number of Physics professors in the 25-34 age group must be 12.