LM wrote:

Each has no. of interns = (M+F)/n

Each has no. of females = (22/100)*F

Each has male interns = x such that => (18/100)*M < x < (22/100)*M

Could you please explain in detail?

LM, it's not "each" but only one correctional facility. One particular correctional facility has 22% of female interns (22/100)*F and has d*M males -> total number of interns in the facility is (22/100)*F + d*M. Since each facility has the same total number of interns (F+M)/((22/100)*F + d*M) has to be a positive integer. Using inequalities I showed that the integer is greater than 4 and less than 6. It has to be equal to 5. Since there are more than 1/5 female interns, d < 1/5, otherwise the facility will have more than 1/5 of all interns which contradicts the condition that each facility has the same number of interns.