Relay Jun’s 수업은몇시예요? to staff as 준이수업은몇시냐고물었어요. Jun asked; he did not answer “three.” The complete reporting sentence is a statement and can end with a period.
Original expression
Reported expression
몇시예요?
몇시냐고물었어요.
장소가교실이에요?
장소가교실이냐고물었어요.
언제시작해요?
언제시작하냐고 / 시작하느냐고물었어요.
방이커요?
방이크냐고물었어요.
준도와요?
준도오냐고 / 오느냐고물었어요.
Nouns take -이냐고 after a final consonant and -냐고 otherwise. A current-action question can be relayed as 시작하느냐고; spoken 시작하냐고 is also used and accepted here. Do not retain -요 inside the reporting ending.