The council may establish a personnel board with authority to administer tests designed to determine the merit and fitness of candidates for appointment or promotion, to conduct hearings upon the appeal of employees who have been suspended, demoted, or discharged, and hear employee grievances. (1917, c. 136, subch. 5, s. 1; 1919, cc. 136, 237; C.S., s. 2787; 1965, c. 931; 1971, c. 698, s. 1.)