The Alexandria City Council approved a $110 million budget and cut a nickel from the property tax rate early today.

The new tax rate of $1.39 per $100 of assessed valuation won't be enough to offset inflation, and the owner of an "average" Alexandria home -- valued at $84,000 -- will pay about $159 more in property taxes. Property values in the city have risen about 20 percent in the past year.

The budget the council approved includes a guaranteed appropriation of $39.5 million for city schools, with a promise of $700,000 more if needed.

The program for the fiscal year starting July 1 also provides for adding 20 police officers to the existing force of 232, the largest police staff increase in five years.

The new budget also will give allcity employes 10 percent raises.

The final budget details were hammered out by the council at a five-hour session that lasted until shortly after midnight today.

For the first time, Alexandria's budget tops $100 million. Spending will be up 17 percent over the $94 million budget for the current fiscal year.

The City School Board had sought $41 million from the council. The $39.5 million figure that was approved reflects the council's long standing feud with the board over spending.

Council member James P. Moran Jr., who proposed placing the additional $700,000 in a special account that the school board can use only with council permission, said he wanted the board to justify its need for extra money. Council members have complained repeatedly that board members fail to keep them informed how money is being spent.

One school board member complained outside the council's meeting that the requirement that the board justify its necessary expenses to get the extra $700,000 is "confusing and insulting."

The school board wanted to give its employes 12.5 percent raises, but the council approved 10 percent raises for them, the same the municipal workers will receive.

The council's salary decision will not necessarily govern the school board, which has authority to arrange its own expenditures. The board could rearrange its spending plans to fund the 12.5 percent raises.

City workers belonging to various labor groups booed when the council approved the 10 percent pay increase. Council member ROBERT L. Calhoun said that with automatic merit raises and fringe benefits the total pay raise for city employes actually amounted to more than 17 percent.

Included in the budget is more than $20 million for such physical construction as the start of a new police/jail complex, completion of the new city courthouse and the remodeling of City Hall. The council killed for this year a proposal to build a professional baseball stadium for the privately owned Alexandria Dukes baseball team.