Acts 16.30,31 And he brought them out and said, "Sirs, what must I do to be saved?" So they said, "Believe on the Lord Jesus Christ, and you will be saved, you and your household."
Since the whole of the Bible is clear that each person is to make their own profession of salvation, how are we to understand these verses.
The Philipian jailer asked a question and Paul answered correctly by telling him that if he believed on the Lord jesus Christ he would be saved. This statement applies equally to all in his household; in other words if each person was to believe they would be saved. It is not one person believing that results in a saved household; but it is that each person in the household has equal opportunity to believe and receive salvation.
Paul answered the question with what he had to do to be saved; but also extending this invitation to anyone else who also would believe. There is no discrepancy between this and any other scripture.