In the following question, a sentence has been given in the active voice. Out of the four alternatives suggested, select the one which best expresses the same sentence in the passive voice. He could have solved the problem.

Introduction / Context:
This grammar question tests your understanding of how to change a sentence from the active voice to the passive voice, especially when a modal verb such as "could" is involved. The original sentence is "He could have solved the problem." You must select the option that correctly expresses the same meaning in the passive voice while preserving tense and sense.

Given Data / Assumptions:

• Active sentence: He could have solved the problem.
• Subject: he.
• Object: the problem.
• Verb phrase: could have solved (modal verb plus perfect infinitive).
• We must convert this to passive voice with the object as the new subject.

Concept / Approach:
When changing a sentence with a modal verb to passive voice, the standard pattern is: object + modal verb + have been + past participle + by + subject. In this sentence, the modal "could" must stay, and "have solved" must change to "have been solved," because the problem is the receiver of the action. The phrase "by him" shows who had the ability to solve the problem. This structure preserves both the possibility and the past time reference of the original.

Step-by-Step Solution:
Step 1: Identify the object in the active sentence: the problem.Step 2: Bring that object to the front to become the new subject of the passive sentence.Step 3: Retain the modal verb "could" and follow the pattern "could have been" for the passive perfect form.Step 4: Change the main verb "solved" to its past participle form "solved" and place it after "been."Step 5: Add the agent phrase "by him" at the end to show who had the ability to solve the problem.Step 6: The resulting sentence is: The problem could have been solved by him.

Verification / Alternative check:
To verify, convert the passive sentence back into active voice. Start with the agent "him," convert it to the subject form "he," keep the modal "could," keep the perfect structure "have solved," and move "the problem" back to object position. This gives you "He could have solved the problem," which matches the original sentence exactly. This confirms that the chosen passive form is correct.

Why Other Options Are Wrong:
"The problem could be solved by him" uses simple modal with base form and removes the perfect aspect, changing the time reference. "The problem could have solved by him" is grammatically incorrect because passive construction requires "have been solved," not "have solved." "The problem could solve by him" wrongly uses the verb "solve" without proper passive auxiliary. "The problem was able to be solved by him" changes the structure and emphasis; it suggests a general ability rather than the specific modal perfect meaning of the original.

Common Pitfalls:
Students often forget to include "been" in passive forms with perfect aspect and modal verbs. Another common error is to copy the active structure directly after the modal, which leads to expressions like "could have solved by" without the necessary auxiliary. Remember that in passive voice, after a modal and "have," you must include "been" before the main verb in its past participle form.

Final Answer:
The problem could have been solved by him.