Explanation:

This question requires us to convert an interrogative sentence (a Wh-question) from Active Voice to Passive Voice. The original sentence is: 'Why did your uncle write such a letter?' **Understanding the Active Voice Sentence:** * **Wh-word:** 'Why' (remains at the beginning in passive voice questions). * **Tense:** Simple Past ('did write'). * **Subject (Agent):** 'your uncle'. * **Object:** 'such a letter'. **Rules for Converting Simple Past Wh-Questions to Passive Voice:** 1. **Wh-word:** The Wh-word ('Why') remains at the beginning. 2. **Auxiliary Verb:** For Simple Past Passive, the auxiliary verb is 'was' (for singular object) or 'were' (for plural object). 3. **Object becomes Subject:** The object of the active sentence ('such a letter') becomes the subject of the passive sentence. 4. **Main Verb:** The main verb ('write') changes to its past participle form ('written'). 5. **Agent:** The original subject ('your uncle') becomes the agent in the passive sentence, preceded by 'by'. 6. **Punctuation:** The sentence remains a question. **Passive Voice Structure (Simple Past Wh-Question):** Wh-word + was/were + new subject (original object) + past participle + by + original subject (agent)? Let's analyze each option: **Option (A): Why was such a letter being written by your uncle?** * **Tense:** 'being written' indicates the Past Continuous Passive tense (e.g., 'Why was such a letter *being* written at that moment?'). The original sentence is in Simple Past, not Past Continuous. Therefore, the tense conversion is incorrect. **Option (B): Why was such a letter written by your uncle?** * **Wh-word:** 'Why' is correctly placed. * **Auxiliary Verb:** 'was' is correct for the singular subject 'such a letter'. * **New Subject:** 'such a letter' is correctly placed. * **Past Participle:** 'written' is the correct past participle of 'write'. * **Agent:** 'by your uncle' is correctly included. This option perfectly follows all the rules for converting a Simple Past Wh-question to Passive Voice. It is grammatically correct. **Option (C): Why did your uncle wrote such a letter?** * **Voice:** This sentence is still in Active Voice. The question asks for Passive Voice. * **Grammar:** Even as an active sentence, 'did' and 'wrote' together is grammatically incorrect. It should be 'Why did your uncle write...'. Therefore, this option is incorrect on multiple counts. **Option (D): Why was such letter been written by your uncle?** * **Article:** 'such letter' is missing the indefinite article 'a' before 'letter'. It should be 'such *a* letter'. * **Tense/Structure:** 'been written' is typically used in perfect passive tenses (e.g., Present Perfect Passive: 'has been written', Past Perfect Passive: 'had been written'). It is not used for Simple Past Passive. The correct form for Simple Past Passive is 'was/were + past participle'. Therefore, the structure is incorrect. **Conclusion:** Option (B) is the only sentence that correctly converts the original active voice Simple Past Wh-question into its passive voice equivalent, adhering to all grammatical rules for tense, subject-verb agreement, and structure. Therefore, option (B) is the correct answer.