Let's analyze the transformation from direct to indirect speech:
Step 1: Identify the reporting verb and tense:
- Reporting verb: "said" (past tense).
Step 2: Change the question in direct speech to an indirect question:
- Direct question: "Are you going to your House?"
- In indirect speech, yes/no questions use "if" or "whether".
Step 3: Apply backshift in tense:
- Present continuous "are going" changes to past continuous "was going".
Step 4: Change pronouns and possessives accordingly:
- "your House" changes to "his house" (since the gatekeeper is talking to "him").
Therefore, the correct indirect speech sentence is:
The gatekeeper asked him if he was going to his house.