Which one of the following options is the correct Indirect Speech of…

The correct answer is Option (3) → The king said that they had managed to deal with the enemies and their treacherous allies.

Direct to indirect speech (statement):

Change	Direct	Indirect	Why
Reporting verb	said, “	said that	“Said” stays “said” for a statement, and the quoted words are joined by “that”.
Pronoun change	we	they	“We” (the king and his people) becomes “they”.
Tense change	have managed	had managed	With a past reporting verb, the present perfect “have managed” moves back to the past perfect “had managed”.
Full sentence	The king said, “we have managed to deal with the enemies and their treacherous allies.”	The king said that they had managed to deal with the enemies and their treacherous allies.

The rest of the sentence ("the enemies and their treacherous allies") stays as it is.

Example: She said, “I have lost my keys.” → She said that she had lost her keys.

Why the Other Options are Incorrect?

Option 1: The king asked that they have managed to deal with the enemies and their treacherous allies for now. — Incorrect.

• "Asked" is used for questions. The king made a statement.
• The tense is not changed: "have managed" should be "had managed".
• "For now" is added. It is not in the original.

Option 2: The king said that they have managed to deal with the enemies and their treacherous. — Incorrect.

• The tense is not changed to "had managed".
• The noun "allies" is missing, so "their treacherous" is left incomplete.

Option 4: The king had said that they had managed to deal with the enemies and their treacherous allies. — Incorrect. The reporting verb itself is changed to "had said". The reporting verb keeps its own tense, and only the reported words change.