About half of the 10-cent, 6.4 percent increase in property taxes approved last week by the Fairfax City Council will go to pay for $900,000 in school repairs and improvements, projects which were to have been funded by the proposed $6.2 million school bond issue voters defeated the day before the council adopted the new budget, according to city spokesman Thomas Welle.

The $25 million city budget for fiscal 1983-84 will add about $100 a year to the average homeowner's tax bill, when the 3 percent inflation in the value of houses is calculated. The budget boosts the property tax rate from $1.15 to $1.25 per $100 of assessed value. The average single-family house in the city increased from $90,000 to $93,000 in value during the past year.

The other half of the 10-cent tax increase will pay for a $1.5 million shortfall created by overly optimistic city revenue forecasts during this year and will add $400,000 to the city employes' retirement fund, which some council members had considered underfunded. At the same time, the council slightly reduced pension benefits for both current and future city employes, benefits considered among the most generous of any municipality in Virginia.

The council also raised the cigarette tax from 7 cents to 10 cents a pack, which is expected to generate an additional $130,000, and in February raised auto tag fees by $5 a car. It did not increase the personal property (auto) tax rate and actually decreased the water-sewer tax by close to $30 a year for residents who use about 20,000 gallons of water per quarter.

The budget adopted by the council knocks out several projects proposed for next year, including synchronized traffic signals for Rte. 123, the widening of Jones Street and a study of a public safety center at City Hall, and it puts off most of the school repairs the $6.2 million bond issue would have funded.

The council put $190,000 in reserve for possible renovation of the John C. Woods School as a public safety center.

While defeat of the school bond issue means that any school improvements must be funded out of annual operating budgets, the defeat does save the city $7.2 million in bond interest over the next 20 years.