In this reported speech question, the direct sentence is The wayfarer said to me, "Do you know the way to the Asiad village", and you must choose the indirect form that correctly reports this yes or no question. Select the alternative that best expresses the same meaning with proper changes in word order and tense.

Introduction / Context:
This question concerns the reporting of a yes or no question in simple present tense. The wayfarer directly asks Do you know the way to the Asiad village. In indirect speech, such questions are usually introduced by asked plus if or whether, followed by a clause in normal statement order. The tense may shift from simple present to simple past because the reporting verb is in the past, and the pronouns must be adjusted to fit the new point of view.

Given Data / Assumptions:

• Direct speech: The wayfarer said to me, "Do you know the way to the Asiad village".
• The reporting verb is said to, which will normally become asked in indirect speech.
• The question is in simple present tense: do you know.
• The pronoun you refers to me, the listener in the reporting clause.

Concept / Approach:
For yes or no questions in reported speech, the structure is asked plus if or whether plus clause. The auxiliary do disappears, and we use normal subject verb order: if I knew. Because the reporting verb is in the past (said to), the simple present know usually becomes simple past knew in the reported clause. The pronoun you turns into I, because the person being asked now tells the story. Therefore, the correct indirect sentence should be The wayfarer asked me if I knew the way to the Asiad village.

Step-by-Step Solution:
First, change said to me to asked me to show that a question is being reported. Second, introduce the reported question with if, because the original is a yes or no question. Third, transform do you know into normal statement order with tense backshift, giving I knew instead of do you know. Fourth, keep the rest of the sentence the same, as the Asiad village remains the destination mentioned. Fifth, combine these elements to form The wayfarer asked me if I knew the way to the Asiad village.

Verification / Alternative check:
To verify, convert the candidate indirect sentence back to direct speech. From The wayfarer asked me if I knew the way to the Asiad village we can reconstruct The wayfarer said to me, "Do you know the way to the Asiad village". The pronoun I returns to you, and the simple past knew returns to simple present know, while if is replaced by the auxiliary do in the question. This symmetry shows that the indirect sentence accurately represents the original question.

Why Other Options Are Wrong:
Option A, The wayfarer asked me if I did know the way to the Asiad village, uses did know, which gives an unnecessary emphasis and is not the usual pattern for reported yes or no questions; simple knew is preferred.

Option C, The wayfarer asked me if he knew the way to the Asiad village, changes the pronoun from I to he, incorrectly suggesting that the wayfarer was asking about his own knowledge rather than mine.

Option D, The wayfarer asked me that if I knew the way to the Asiad village, is ungrammatical because that and if are not used together in this way in reported questions.

Common Pitfalls:
Learners sometimes keep the auxiliary do or does in reported questions, leading to forms like if I do know, which is incorrect. Another frequent mistake is forgetting to change pronouns and tenses to match the new perspective and time frame. Using a clear rule that yes or no questions become if or whether plus subject and verb in normal order greatly reduces such errors.

Final Answer:
The indirect question that correctly reports the wayfarer's enquiry is The wayfarer asked me if I knew the way to the Asiad village.