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)

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