Choose the correct transformation of the given sentence in Indirect S…

The correct answer is Option (1) → The librarian asked the boys why they were talking so loudly in the reading room.

Changing a “why” question into indirect speech:

Change	Direct	Indirect	Why
Reporting verb	said to the boys	asked the boys	The librarian puts a question. So “said to” becomes “asked”.
Joining word	“ ” (quotation marks)	why	The question word “why” itself joins the two parts. No “that” or “if” is added.
Word order	are you talking	they were talking	The question order “are you” changes to the plain order, subject first. The “?” goes.
Tense change	are talking	were talking	“Are talking” is in the present continuous. The present continuous is formed with am / is / are + V-ing. After the past “said” it becomes the past continuous “were talking”. The past continuous is formed with was / were + V-ing.
Pronoun change	you	they	The boys are the people spoken to. In the report “you” becomes “they”.
Full sentence	The librarian said to the boys, “Why are you talking so loudly in the reading room?”	The librarian asked the boys why they were talking so loudly in the reading room.

What, where, when and how join a reported question in the same way. Example: Mom said to me, “Where are you going?” → Mom asked me where I was going.

Why the Other Options are Incorrect?

Option 2: The librarian asked the boys why were they talking so loudly in the reading room. — Incorrect. “Were they” keeps the question order. A reported question puts the subject first: “why they were talking”.

Option 3: The librarian asked the boys why they are talking so loudly in the reading room. — Incorrect. “Are talking” is left unchanged. After the past “said” it becomes “were talking”.

Option 4: The librarian asked the boys that why they were talking so loudly in the reading room. — Incorrect. “That” and “why” are two joining words together. A reported question is joined by the question word alone.