Step 1: Rule.
For interrogative sentences in indirect speech, "said to" becomes "asked," and tense shifts back (is → was).
Step 2: Options check.
(A) Correct — matches rule: "asked… if he was going out."
(B) Wrong — uses future tense "will ask."
(C) Wrong — grammatically incorrect.
(D) Wrong — "went out" changes the tense meaning.
Step 3: Conclusion.
Answer is (A).