The Montgomery County Council adopted an operating budget of $967.6 million yesterday, a budget that is 9.6 percent greater than current spending and includes money to improve day care for children, the elderly and retarded persons.

Before approving a budget that is $84.4 million higher than the current spending level, the council trimmed $787,000 from County Executive Charles Gilchrist's proposed budget. But Gilchrist said he was pleased that the council retained much of his social service initiative, which includes day care and other services for the disadvantaged.

The council also adopted a six-year capital improvements plan designed to meet road needs in the booming upcounty area, provide renovations for older county schools, build nine elementary schools and plan for two new high schools near Gaithersburg by 1990. The billion-dollar program includes a first-year cost of $256.4 million.

How the spending plans, which take effect July 1, will affect taxpayers was unclear yesterday as county financial analysts wrangled with the new figures approved by the council. A tax rate will be set by mid-June.

Based on Gilchrist's budget recommendations, the tax rate would have fallen seven cents, from $3.05 for every $100 of assessed property value, to $2.98, according to the county's Office of Management and Budget.

Higher real estate assessments, however, are likely to push up tax bills. Under Gilchrist's proposal, owners of $100,000 houses could expect to pay between $24 and $108 more in taxes, or tax bills ranging from $1,499 to $1,874, next year.

In agreeing to provide all the social services that Gilchrist sought in his proposal, the council helped make up for a decline in federal funds in those areas.

The county will spend $3 million to subsidize day care centers, establish 25 all-day kindgarten programs and add hundreds of thousands of dollars to programs to combat child abuse and encourage better nutrition for children. Another $744,000 will be spent on residential and day care programs for the mentally ill.

One of the biggest cuts in the operating budget submitted by Gilchrist in March was funding for schools. The Board of Education had asked for $1.7 million to hire additional teachers to allow for smaller classes.

School Superintendent Wilmer S. Cody reacted with pleasure, however. "We didn't get quite what we wanted . . . but it allows us to not only maintain the quality of education, but to improve."

The council cut about $400,000 from the request for extra teachers and $464,000 from administrative costs that would have included teaching supervisors. At the last mintue, another $41,000 was taken from the board's retirement budget, after council members sharply attacked a recently negotiated contract between the board and its employes that offered incentives for early retirement. A similar plan for county police was rejected.

"As an economist, it seems to me the county is not better off by paying people not to work," said council member Neal Potter during several hours of criticism of the school board.

"Somebody, somewhere, has to think about the big picture," council member Esther Gelman said. "The school board is not elected to think about the implications of what they're doing."

School board president Robert Shoenberg, who described the maneuver as "budgetary retribution," said some members apparently were concerned that such a plan might cost the county money, "but it's just not true. We have tried to demonstrate why it was necessary, but . . . some members have a 'don't confuse me with facts, my mind's made up' attitude." However, Shoenberg called the capital and operating budget allocations "good and very generous."

Gelman congratulated the council for "sending a message to the school board" about the retirement plan, and for turning back a similar plan for county police officers. However, the council's approval of a new police contract, which closed a proposed early-retirement "window" in favor of accelerating a pay schedule for higher-paid senior officers, was criticized by Gilchrist.

Gilchrist pointed out that the council contract added $85,000 to the police budget over the next two years, and said the original bargained contract, which was rejected 4-3 by the council last month, would have saved the county a modest sum through 1990.

The capital improvements buget also focused on the needs of the school system. Gilchrist's recommendation that the county spend $162 million for school construction was increased substantially by the council, which agreed with a school board request for new elementary schools and two high schools for upcounty -- Watkins Mills and Quince Orchard.

Gilchrist's recommended that Quince Orchard High be funded by September 1988 and Watkins Mills be deferred until the 1990s. But the council made funds available for one of the schools to be opened in 1988 and the other in 1989, with the school board to decide which one should open first.

Other capital improvements approved included: extending Woodmont Avenue south from Montgomery Lane to Leland Street in Bethesda; building a regional swim center between Rockville and Bethesda and extending Montrose Road west from Seven Locks Road to Falls Road.

In a marked change from the way it normally pays for new roads and schools, the council voted to use $17.4 million on hand instead of selling general obligation bonds. Gilchrist had proposed using at least $8.6 million in cash for such projects, in an effort preserve the county's AAA bond rating.