let us suppose total number of men working in the department is m
and total number of women working in the department is w

Of the total women working in the department let us assume those that have a phd is A
hence those that do not have a phd = A+10

we are given 1/3 M have phd
hence 2/3 M do not have a phd

we have 1/3 M + A = 14 (those with phd).....i
and 2/3 M + A+10 = 30 >> 2/3 M + A = 20 (those without phd)...ii

subtracting eqn i from ii we get,
1/3 M = 6 hence, M = 18

Total number of people that work in the department = 44
Total number of Men that work in the department = 18
hence, total number of women working in the department = 44-18 = 26
(c)
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes