How have you solved this difficult sum in passive voice?

The passive voice transformation of the question "How have you solved this difficult sum?" is "How has this difficult sum been solved by you?" This restructuring shifts the focus from the doer of the action (you) to the recipient of the action (the difficult sum).

Understanding Passive Voice in Questions

Passive voice is a grammatical construction where the subject of the sentence receives the action rather than performing it. In questions, this often involves rearranging the auxiliary verbs and the subject-object relationship.

Active vs. Passive Structure

Active Voice: Emphasizes who or what performed the action.
- Example (Active Question): How have you solved this difficult sum?
  - Subject: you
  - Verb: have solved (Present Perfect Active)
  - Object: this difficult sum
Passive Voice: Emphasizes the action itself and its recipient, making the object of the active sentence the new subject. The original subject, if mentioned, is usually introduced by "by."
- Example (Passive Question): How has this difficult sum been solved by you?
  - New Subject: this difficult sum
  - Verb: has been solved (Present Perfect Passive)
  - Agent: by you

Steps for Transforming Active to Passive Voice (Present Perfect Questions)

To accurately convert an active voice question in the present perfect tense to passive voice, follow these steps:

Identify Key Components: Locate the question word (e.g., "How"), the auxiliary verb ("have"), the subject ("you"), the main verb ("solved"), and the object ("this difficult sum").
Make the Object the New Subject: The object of the active sentence ("this difficult sum") becomes the subject of the passive sentence.
Adjust Auxiliary Verb:
- Since the new subject ("this difficult sum") is singular, change "have" to "has."
- Add "been" before the past participle of the main verb.
Use Past Participle: Retain the past participle form of the main verb ("solved").
Introduce the Agent (Optional): If the original subject ("you") is important, introduce it with "by" at the end of the sentence ("by you").
Maintain Question Word: Keep the original question word ("How") at the beginning.

Example Transformation:

Let's break down the transformation of "How have you solved this difficult sum?":

Original Active: How have you solved this difficult sum?
Step 1 & 2 (New Subject): How has this difficult sum ...
Step 3 & 4 (Verb Phrase): How has this difficult sum been solved ...
Step 5 (Agent): How has this difficult sum been solved by you?

This structured approach ensures that the grammatical integrity of the passive voice is maintained while effectively answering the query. The core idea is to shift the subject, highlighting the outcome on the object. For instance, in understanding such shifts, one might encounter formulations like 'How have this sum been solved by you?' to illustrate the object's new role and the structure of the present perfect passive.