The Prince William County Board of Supervisors yesterday raised the county tax rate by 21 per cent - an increase that will add $150 to the $725 in property taxes now paid by the owner of a $50,000 home.

The new tax rate of $5.25 for each $100 of assessed value, is the result of inflation, reduced state and federal revenues, and the loss of the tax and federal revenues, and the loss of the tax base of the City of Manassas, which became an independent city last summer.

Nearly three-quarters of the county's local revenue comes from the property tax. Despite intensive efforts to cut the county's $90.8 million budget over the past few weeks, the supervisors voted yesterday to raise the tax rate rather than cut the county school budget by an additional $2 million.

School board member Herbert Saunders told the board that a $2 million cut would cause irreparable damage to the schools and would force elimination of all music, ar and physical education programs not required by state law.

The final $5.25 rate was passed 4 to 3 over the objection of Supervisors Andrew J. Donelly, James Byrd, and T. Clay Wood.

Donnelly, citing inflation and increasing energy costs said, "there are thousands of people in this country - as many as 50 per cent of the people - who can't afford an increase (to this level). This year we're going to have to live with less."

Supervisor James T. McCoart, who voted with Alice E. Humphries, Donald L. White and Kathleen K. Seefeldt in support of the schools, warned that the deeper cuts would leave Prince William children unable to compete with graduates of other ara jurisdications.

The new county budget for the fiscal year that starts July 1 is up 3 per cent over last year to the $90.8 million figure. About $55.7 million of this comes from local sources, with the rest being paid fro from state and federal revenues.

The Board's action leaves Prince William with what county financial officials consider a true tax rate of $1.49 for each $100 of property.

This rate is figured by calculating how much the tax would be if it were based on property assessed at 100 per cent of its fair market value. Prince William now assesses real estate at an official rate of 33 per cent, and officials estimate that actual assessments are about 15 per cent lower than the official rate calls for.

The comparable tax rate in the Washington suburbs of Maryland - if figured on 100 per cent of the assessed value of homes rather than the official 50 per cent assessment rate - would be: Prince Georges County, $1.68; and Montgomery County, $1.96. The comparable rate in the District is now $1.83.

Other Virginia jurisdictions are considering setting true tax rates as follows, based on Prince William esitments: Alexandria $1.79, Fairfax City $1.75, Fairfax County $1.74, Arlington $1.51, and Loudoun $1.32. The actual rates are ecpected to be lower tha those levels.

The county also changed the tax rate on personal property from $5.65 based on 40 per cent of value to $4 based on 100 per cent of value. The result will be a near doubling in the tax on cars, trailers and other personal property.