In this reported speech question, the direct sentence is The clerk said to the visitor, "Shall I ask these people to wait for you", and you must select the indirect version that correctly reports this offer or suggestion. Choose the option that best transforms the question into an indirect yes or no question while keeping the meaning intact.

Introduction / Context:
This question examines the conversion of a direct yes or no question with shall into indirect speech. The clerk is making an offer or suggestion by asking Shall I ask these people to wait for you. In indirect speech, such questions usually become if clauses with should rather than shall, as should is typically used to express polite offers or suggestions in reported form. The reporting verb asked the visitor introduces the indirect question.

Given Data / Assumptions:

• Direct speech: The clerk said to the visitor, "Shall I ask these people to wait for you".
• The structure is a yes or no question with shall I as the auxiliary.
• The reporting verb said to becomes asked in indirect speech.
• The pronouns and demonstratives may change: these people may become those people, and you may become him.

Concept / Approach:
When reporting a question with shall I, which expresses an offer or suggestion, English often uses should in the indirect form. The question form with inversion shall I ask becomes a statement form introduced by if, such as if he should ask. The pronoun I becomes he, referring to the clerk, and you becomes him, referring to the visitor. Demonstratives often shift according to distance, so these people can become those people. Therefore, our task is to select the option that uses asked the visitor if he should ask those people to wait for him, preserving the meaning and applying the usual changes.

Step-by-Step Solution:
First, identify the main components: the reporting clause The clerk said to the visitor and the question Shall I ask these people to wait for you. Second, change said to into asked to reflect that a question is being reported. Third, transform the question into an if clause and replace shall with should, in line with standard reported speech for offers. Fourth, shift pronouns: I becomes he (the clerk) and you becomes him (the visitor), while these people changes to those people. Fifth, assemble the indirect sentence as The clerk asked the visitor if he should ask those people to wait for him.

Verification / Alternative check:
To verify, imagine the indirect sentence being converted back to direct speech. From The clerk asked the visitor if he should ask those people to wait for him you can reconstruct The clerk said to the visitor, "Shall I ask these people to wait for you". The pronoun shifts and demonstrative changes reverse naturally, and should returns to shall as the auxiliary of the direct question. This back conversion shows that the chosen indirect form accurately represents the original meaning and structure.

Why Other Options Are Wrong:
Option B, The clerk asked the visitor if he shall ask these people to said for him, contains grammatical errors, including shall in reported speech and the incorrect phrase to said for him.

Option C, The clerk asked the visitor if he had asked those people to wait for him, changes the time reference and implies a past completed action instead of an offer about a future action.

Option D, The clerk told the visitor that he should ask these people to wait for him, reports a statement rather than a question and does not use if to introduce the indirect question, so it does not match the original form.

Common Pitfalls:
Learners often forget to change shall to should in reported questions, or they fail to adjust pronouns and demonstratives according to the new point of view. Another common error is to report questions as statements by dropping the if or whether marker. Practising with multiple examples of shall I questions and their indirect forms helps in mastering this pattern.

Final Answer:
The correct indirect form that reports the clerk's offer or suggestion is The clerk asked the visitor if he should ask those people to wait for him.