Let the number of directors equals to N_d and the number of managers equals to N_m, the average salary of the total population equals to x, we can have the following:
[N_d(15,000+x)+N_m(x-5,000)]/[N_d+N_m]=x
==>15,000N_d-5,000N_m=N_d+N_m
==>Thus, we can solve for the percentage of directors through this equation.