In the following question, a sentence is given in direct speech. Select the option that best expresses the same sentence in indirect (reported) speech. The children said, "They were busy playing thus they did not notice the stranger."

Introduction / Context:
This question checks the ability to convert a past continuous and past simple combination in direct speech into correct reported speech. The original sentence explains why an action did not happen, so the reported version must preserve this cause and effect while obeying tense sequence rules. Mastery of reported speech is essential for clear academic and professional English.

Given Data / Assumptions:

• Reporting verb: "said" in simple past.
• Direct speech: "They were busy playing thus they did not notice the stranger."
• The pronoun "they" in the quote refers to the same group as "the children".
• Verb phrases: "were busy playing" (past continuous) and "did not notice" (simple past).
• Connector "thus" or "so" indicates a reason.

Concept / Approach:
With a past reporting verb, past continuous usually changes to past perfect continuous, and simple past normally changes to past perfect. This gives the sense that the reported actions were already completed at the time of reporting. The pronoun "they" continues to refer to the children, so it remains "they". The conjunction "so" is commonly used in reported speech instead of "thus" to sound more natural in many exam patterns, although both express cause. The indirect sentence should be a smooth statement without quotation marks.

Step-by-Step Solution:
Step 1: Keep the reporting clause "The children said" and attach the conjunction "that". Step 2: Convert "they were busy playing" to "they had been busy playing", changing past continuous to past perfect continuous. Step 3: Replace "thus they did not notice the stranger" with "so they had not noticed the stranger", changing simple past "did not notice" to past perfect "had not noticed". Step 4: Combine everything into "The children said that they had been busy playing so they had not noticed the stranger." Step 5: Check that the reason (being busy) still clearly explains why the stranger was not noticed.

Verification / Alternative check:
We check tense sequence, pronoun use, and logical flow. Both verbs in the original quote refer to actions in the past relative to the reporting. The past perfect and past perfect continuous forms correctly show that they were completed before the time of reporting. The sentence remains logically sound and clear, and no information has been added or removed. This confirms the correctness of the reported form.

Why Other Options Are Wrong:
Option A uses "have not noticed" which is present perfect and does not agree with the past time context and the past reporting verb. Option C mixes "have been busy playing" with "had not noticed", which produces an inconsistent timeline. Option D keeps both verbs in present perfect forms, which is not appropriate because the report clearly refers to a finished situation in the past.

Common Pitfalls:
Learners sometimes change only one verb and forget to backshift the second verb in a compound sentence. Another error is using present perfect after a past reporting verb, which breaks the rule of sequence of tenses. Some students also overlook the need to retain the reason connector, which can change the nuance of the sentence. A reliable technique is to list each verb and check whether it needs backshifting, then verify that all clauses fit the same time frame.

Final Answer:
The correct reported sentence is The children said that they had been busy playing so they had not noticed the stranger.