-(으)냐고 하다

You use it to pass on a question someone asked: "X asked whether / what / where …".

인용·전달Quoting & reporting

Han: The friend asked a question, so it must be reported with -냐고; -다고 is for reporting statements.

Examples

어떤 분이 약국이 어디에 있냐고 해서 알려 드렸어요.Someone asked where the pharmacy was, so I told them.

친구가 저한테 주말에 시간 있냐고 물어봤어요.My friend asked me if I had time on the weekend.

엄마가 전화해서 밥 먹었냐고 하셨어요.Mom called and asked whether I had eaten.

선생님이 이게 누구 가방이냐고 물으셨어요.The teacher asked whose bag this was.

-(으)냐고 하다vs-다고 하다-다고 reports a statement, -냐고 reports a question: 비가 온다고 했어요 (said it's raining) vs 비가 오냐고 했어요 (asked if it's raining).

V/A+(으)냐고 하다 (V: 냐고; A with final consonant: 으냐고 or 냐고)

N+(이)냐고 하다

past: 았/었냐고

가다 → 가냐고 해요, 먹다 → 먹냐고 했어요, 작다 → 작으냐고/작냐고 했어요, 학생 → 학생이냐고 했어요, 의사 → 의사냐고 했어요

Tense of the original question goes before 냐고 (갔냐고, 갈 거냐고); the tense of the reporting verb 하다/묻다 shows when the question was asked.
It is for questions only; statements use -다고 하다, suggestions -자고 하다, commands -(으)라고 하다.
With verbs, speech usually uses 냐고 (먹냐고); formal writing often uses 느냐고 (먹느냐고). Don't attach 냐고 to a polite ending: not 가요냐고.
In everyday speech 묻다/물어보다 is often used instead of 하다, and 냐고 하다 is often shortened to 냬요 (= 냐고 해요).

Wrong: ~~친구가 저한테 어제 뭐 했다고 물어봤어요.~~

Right: 친구가 저한테 어제 뭐 했냐고 물어봤어요.

The friend asked a question, so it must be reported with -냐고; -다고 is for reporting statements.

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