In March, Betty Charleton complained that she was being taxed unjustly by Fairfax County for tutoring children in reading at her Mount Vernon home.

This week, the Fairfax County Board of Supervisors agreed with her and revoked a controversial $10 minimum business and professional liscense tax on county residents who earn $5,000 or less from working out of their own homes.

The county expects to lose about $32,000 by revoking the tax and giving refunds to those who already have paid it. The county also plans to refund penalties charged residents who had not paid the minimum tax after it was established Jan. 1, 1977.

"Nuisance taxes are bad, and we should get rid of them whenever we find them," said Fairfax Board Chairman John F. Herrity, in thanking Charleton for bringing to the board's attention the hardships created by the minimum tax.

About 3,000 county residents came under the minimum tax requirement for work such as dressmaking, tutoring, laundering and babysitting.

Charleton still must pay county taxes on her average income, which was above the $5,000 minimum. For the past three years, her income has ranged from $5,800 to $6,000 a year because the county included earnings from occasional teaching jobs for the Navy in Crystal City as well as the tutoring she does in her home. In addition to state and federal taxes, Charleton said she paid $121 in taxes to Fairfax County this year.

What they did is a step in the right direction, and I'm very pleased," Charleton said. "But my particular problem still has to be solved."

But the revocation of the minimum tax frees Dorothy Samenow of Falls Church, another reading tutor, from paying the county $20.24 in taxes and penalties because her income of $1,729 from teaching in her home last year was less than the $5,000 minimum.

"I could use that $20 to buy books or equipment for the kids I'm teaching," said Samenow. "That tax really discouraged people from giving worthwhile services they really wanted to give."

Another irritation for those who paid the minimum tax was that the county discovered their earnings through state income tax forms they had filed.

"There are plenty of people who don't file state taxes on their work," Samennow said. "The county tax on top of it all sort of said maybe it's not so good to be so honest."