HVC test - the antibodies are formed about 8th week. Takes time in few individuals. Duration of the tests being positive is about 8th - 12th week.
I can only speak for hepatitis C. The average time to develop antibodies in people with a good immune system is 11 weeks. If people have a suppressed immune system such as in HIV, it can take many months to develop antibodies. People who believe they have been exposed can breathe easy by the 12th week but should always test again at 6 months. If there is a need to know sooner, an HCV/RNA by PCR test can be done as it will find actual virus usually by 3 weeks.