A sentence has been given in Direct/Indirect Speech. Out of the four given alternatives, select the one which best expresses the same sentence in Indirect/Direct Speech.
“Are you going to eat with us?” he asked.
He asked me if I was going to eat with them.
He asked whether he was going to eat with them.
She asked me if he was going to eat with them.
The quoted part is in the present continuous tense (are you going) => we will have past continuous tense (was going) in the reported speech. You has been used => it changes to I. Thus, Option 1) is the correct answer.
HE asked = rule out 4).