The District is renovating a building at 11th and K streets NW to use as a "transition house" for young working adults to help them become independent of city assistance, D.C. Social Services Commissioner Audrey Rowe said recently.

The program, which is scheduled to begin June 1 and will cost $1.4 million, would be similar to the old YWCA system or youth hostel where young people would rent rooms and share eating facilities, Rowe said.

The apartment building will house 70 foster-care wards, single mothers and persons coming out of the juvenile justice system in efficiency apartments with a common cafeteria. Each young person must be employed, and the rent will be a percentage of net income, Rowe said.

The city is leasing the building and management will be contracted out. City employes will provide counseling services during the day for the 19-to-24-year-olds, who are supposed to be learning how to live on their own.

"We will give them the kind of support that people get when they leave their families," Rowe said.

Mayor Marion Barry's fiscal 1986 budget includes $1.4 million for the program.

Nancy Smith of the nonprofit Child Advocacy Center expressed qualms about the plan. A scattered site approach would be better, she said, "so you aren't creating a little ghetto of kids." Putting small children in the same building with youths coming from the delinquency system could create problems, she said.

"Can you imagine the drugs? It boggles the mind," she said.

Two years ago when the budget was tight, Mayor Marion Barry proposed ending foster care for about 200 wards who were 19 and 20 years old. But the city decided these wards needed help in moving into living on their own, and the Department of Human Services started developing "bridge" programs.

Meanwhile, the D.C. auditor's office has concluded that the city's foster care system has improved substantially since 1981, when the auditor found that wards were getting "lost" in a system that could not keep track of them.

The city expects to have 2,150 foster-care wards next year, and the budget proposed increasing funding by $5.5 million to $20.2 million in fiscal 1986. Most of the increase would make up for funds from the federal government and the D.C. school system that the city had hoped to get but which never came through. The transitional house, which would include older foster-care wards, is funded under a separate budget.

The latest auditor's review, a follow-up to the 1981 report, concluded that more needs to be done to keep 12-to-19-year-old wards from being moved frequently between foster homes and group homes. Since the 1981 report, a statistical monitoring system has been put into place, the report said, but data still are often incomplete or inaccurate.

In a response to the auditor's findings, included in the same report, Department of Human Services Director David E. Rivers said various actions were being taken:

* A foster home recruitment committee was formed to identify foster care needs.

* Training sessions for foster parents are planned.

* A task force is to be appointed to identify causes of problems in foster care placements, such as emotional instability or drug abuse.

* Profiles of prospective foster parents and children will be computerized.

Rivers said the department planned to transfer foster-care wards 19 and older to the city's general public assistance (GPA) program, as recommended by the auditor, to save $200,000 a year.

But Rowe said this only applied to those that are handicapped and are to receive this assistance until they get into the Supplemental Security Income program.