The plaintiffs, thirteen police officers of Watertown, have appealed from a final decree of the Superior Court. At issue is the validity of a by-law of the town purporting to require overtime pay at straight time rates for hours worked over forty a week. The final decree declared the by-law invalid. The record on appeal is an agreed record under Buie 4 of the Buies for the Begulation of Practice before the Full Court, 328 Mass. 695.
The by-law was adopted at the town meeting held in March, 1964; at the meeting of March 25, 1965, it was so amended that the provisions relied on by the plaintiffs were superseded. Two provisions of the by-law were applicable. Chapter 10, § 9, provided that the “work week for full-employment in each occupational group shall be . . . Public Safety Group Police Classes *40 Hours . . . * Which may be computed as the average work-week for an employee over a seven week cycle.” Chapter 10, § 11 (f), under the title “Public Safety Group,” provided, so far as relevant, “An employee occupying a position in this group shall receive compensation, except for court appearances, for hours worked in excess of his established work week at straight time determined as follows: (1) By dividing his weekly rate by 40 if his position is in one of the police classifications.”
The by-law (c. 10, § 1) stated that it was established pursuant “to the authority contained in Sections 108A and 108C of . . . [G. L. c. 41].”
*624General Laws c. 41, § 108A, as amended through St. 1960, c. 87, provides that a town by by-law may establish “a plan classifying any or all positions, other than those filled by popular election and those under the direction and control of the school committee, into groups and classes” and may establish “a plan establishing minimum and maximum salaries to be paid to employees in positions so classified . . ..” Section 1080, inserted by St. 1954, c. 295, § 2, provides that “A town may consolidate, in a single chapter or article, all provisions of its by-laws pertaining to the administration of its personnel, including,- among other things, . . . the plans established pursuant to section one hundred and eight A of this chapter, and any by-laws adopted pursuant to section twenty-one A of chapter forty . . ..” General Laws c. 40, § 21A, inserted by St. 1951, c. 798, § 5, provides: “A town . . . may establish the hours, days and weeks of work and the hours, days and weeks of leave without loss of pay . . . for any or all employees of such town . . . other than those appointed by the school committee; provided, that the number of working hours, days or weeks so established shall not exceed . . . the number prescribed by any general or special law applicable to such town . . . on [January 1,1952].”
We are of the opinion that G. L. c. 40, § 21 A, authorized the provisions of c. 10, § 9, of the by-law fixing the regular hours of work Of police officers at forty. No statute applicable in Watertown placed the authority elsewhere or prescribed other hours for police officers.
Watertown has not accepted three statutes which would be effective only if accepted: (a) G. L. c. 41, § 97 (“ [T]here shall be a police department established under the direction of the selectmen, who shall . . . fix . . . [the] compensation [of the chief and officers] in an amount not in the aggregate exceeding the annual appropriation therefor”); (b) G. L. c. 41, § 97A (“a police department established by the selectmen . . . under the supervision of . . . the chief of police” with compensation fixed by the selectmen as under § 97; (c) G. L. c. 147, § 17B (“services of all regular *625or permanent police officers . . . shall be restricted to five days and to forty hours in any one week”).
The statutory provision applicable in Watertown is Gr. L. c. 41, § 96: “Selectmen may appoint police officers, who shall hold office during their pleasure.” Under this statute whether police officers are to be paid is for the town to determine. Meader v. West Newbury, 256 Mass. 37, 40. The town’s decision under c. 40, § 21 A, that the regular work week should be forty hours did not invade the function of the selectmen or the chief appointed by them in their full administrative control of the department. As to such control, see Adams v. Selectmen of Northbridge, 253 Mass. 408, 409-410; Ryan v. Marlborough, 318 Mass. 610, 612. According to the statement of agreed facts incorporated in the appeal record, the selectmen from time to time have issued rules and regulations for the government of the police department and the chief of police, since at least 1948, has scheduled the days and hours of duty for all police officers. The town’s establishment of the regular work week does not impede the chief in regularly scheduling more than forty hours of required working time a week. On the contrary, the by-law recognizes that there may be such scheduling and provides for its recompense. The by-law is primarily a compensation plan and the hours of the police officers are fixed for purposes of determining compensation. It does require that for their annual compensation of $6,150 police officers are regularly to work not less than forty hours a week and that for hours over that number they receive additional compensation. These are appropriate provisions of a compensation plan. The agreed facts show that the plaintiffs, in the period for which claim is made, regularly worked more than forty-six hours and forty minutes a week, without compensatory time off for hours over forty.2
*626The defendants contend that, nevertheless, the by-law was inconsistent with a statute that makes express provision for compensating police officers who work in excess of their established hours, and which in this respect, it is asserted, has occupied the regulatory field. General Laws c. 147, § 17C, inserted by St. 1956, c. 349, provides: “If a regular police officer in the service of a city or town which has not accepted section seventeen B shall be required to be on duty for any period in excess of his regular hours of duty as from time to time established, he may be given time off equal to such period of overtime duty or, if time off cannot be given by reason of a personnel shortage or other cause, he may be paid for such period of overtime duty at such an hourly rate as may be determined by the authority in charge of the police department, which rate shall in no event be less than the hourly rate of his regular compensation for his average weekly hours of regular duty.3
Section 170 is in permissive terms. We do not reach the defendants’ contention that, nevertheless, the statute is to be construed as mandatory. We hold that this statute, even if so construed, does not so occupy the field as to bar reasonably consistent municipal regulation under G. L. c. 41, §§ 108A and 1080, and c. 40, § 21A. Compare Dudley v. Cambridge, 347 Mass. 543, 544. We hold also that the bylaw was reasonably consistent with § 170.
The power given to the town in c. 41, §§ 108A and 1080, *627and c. 40, § 21A, is plenary and basic. The scheme of these statutes is for a plan that is to have general application in all departments other than the school department and that establishes mutually consistent rates and plans of compensation. See, for example, c. 41, § 108C, in its provision for “a personnel board or other agency [established] for the purpose of administering said plans or other provisions of its by-laws pertaining to personnel, determining any questions arising thereunder, and advising the town in any matters pertaining thereto.”
The authority given by these statutes to fix hours and compensation includes, by reasonable implication, authority to provide for overtime compensation. Chapter 147, § 17C, could not be construed to take away from the town authority in respect of regular compensation. If c. 147, § 17C, has taken away the power in the town to include in its compensation plan any provision for overtime compensation, it has left the basic statutes authorizing compensation plans incomplete in their operation, and has made a plan adopted thereunder incomplete and imperfect.
We do not discern such an intent in c. 147, § 17C. We think it is to be construed to avoid the effect of carving out of the authority to make a compensation plan for “all positions, other than those filled by popular election and those under the direction and control of the school committee,” the authority to provide for the overtime compensation of police officers.
Construing § 170 so as to give effect to the express and strongly implied intention of the other group of statutes, we find no essential inconsistency. The rate of pay for overtime specified in the by-law conforms with the minimum specified in the statute. The statute deals with compensation for work “in excess of . . . regular hours of duty as from time to time established.” That was the subject of the by-law. Although the rate of compensation to be paid for overtime was not, in the by-law, “determined by the authority [administratively] in charge of the police department,” the rate was determined by the authority *628(that is, the town meeting) in charge of determining police compensation.
The omission in the by-law of the provision for time off (specified in the statute as the compensatory adjustment unless such time off “cannot be given by reason of a personnel shortage or other cause”) created no conflict between the by-law and the statute. The statute in this aspect gives the administrative head of the police flexibility in operating the department. The statute for determining whether forty hour weeks have been worked under the bylaw permits averaging the hours worked in a reasonable number of weeks. The by-law did not bar this practice. Application of the statutory scheme would not diminish the plaintiffs’ claim now presented. That claim is for compensation for hours of work in excess of forty regularly required, week after week, and for which compensatory offsetting hours were not granted. See fn. 2.
We notice two other points of the defendants. The 1964 by-law (c. 10, § 10 [a]) provided: “Upon adoption of this amended by-law . . . the rate of each eligible employee occupying a position in the classification plan shall be adjusted retroactive to January 1 of the year of adoption.” We reject the defendants’ contention that retroactivity of the overtime rate to January 1,1964, was illegal. In so far as the new by-law adjusted the rate of compensation upward it was authorized by G-. L. c. 41, § 108A: “A town may ... by by-law provide that salary and wage increases . . . under a salary plan . . . shall be retroactive to the beginning of the financial year.” The regular police were in the Civil Service, and the insufficiency of the budget appropriations cannot be set up as an excuse for not paying compensation at the rate lawfully fixed. Allen v. Lawrence, 318 Mass. 210, 215.
The final decree is reversed. A decree is to enter declaring that the plaintiffs are entitled to overtime compensation in accordance with c. 10, § 11 (f), of the by-laws of the town for the period in which it was applicable.
So ordered.
“ The aforesaid schedules of hours and days of duty have required the plaintiffs to perform hours of duty totaling more than forty-six hours and forty minutes per week (computed as an average over each seven week period prior to deducting hours of duty, in excess of forty hours per week, not performed due to sickness, injury or vacation) for which the plaintiffs have re*626ceived only their regular weekly rate of compensation. Thus, each plaintiff has performed, after the effective date of the aforesaid new Chapter 10 of the By-Laws, hours of duty in excess of forty hours per week (after deducting hours of duty in excess of forty hours per week not performed due to sickness, injury or vacation) which have not been compensated as overtime. ’ ’
The defendants suggest that this should be read in the light of § 17B (not adopted in Watertown) which provides: ‘1 *Notwithstanding the provisions of any general or special law to the contrary, the services of all regular or permanent police officers of every city and town which accepts this section shall be restricted to five days and to forty hours in any one week; provided, that service in excess of the aforesaid days and hours may be authorized by the police commissioner, chief, superintendent or other officer or board at the head of the police department of any such city or town and the officer performing such additional service shall be compensated at the hourly rate of his regular compensation for his average weekly hours of regular duty or such higher rate as may be determined by the person or persons authorized to establish pay scales in the respective police departments. ’ ’