I’m a bit confused by Acts 16:31 when the jailer wend to Paul and Silas asking what must he do to be saved. They responded by saying “Believe in the Lord Jesus, and you will be saved-you and your household.” This appears as if Paul and Silas were saying if this Jailer believes then he will be saved with his house. If that is the case then how can I be saved and my house be saved through my believing, what if they do not accept the Lord on their own?
Accepting salvation on behalf of another is not permitted. As far back as the Book of Exodus when each one had to gather enough manna for his own needs (Exodus 16:16), the principle of everyone having to ask for themselves was established. Remember, Jesus said the manna was symbolic of Him (John 6:32-35), This “ask for yourself” principle was continued in New Testament passages like Matt. 7:7-8, Romans 10:13 and others.
Acts 16:32 says Paul and Silas spoke the Word of the Lord (presented the Gospel) to the jailer and to all the others in his house, and verse 33 says he and all his family were baptized. This could only have happened if everyone asked to be saved.