In the sentence "The man disappeared after he was rescuing a boy from drowning.", the underlined verb phrase needs correction. Choose the option that best improves the underlined part, or select No improvement if the sentence is already correct.

Introduction / Context:
This sentence improvement item checks whether you can choose the correct tense and aspect to show the order of two past actions. The sentence describes a man who disappeared and also performed a rescue. The verb phrase after he was rescuing a boy from drowning is incorrect because it uses the past continuous in a way that does not clearly mark the completion of one action before another. You must select the form that shows that the rescue was completed before the disappearance.

Given Data / Assumptions:

• Sentence: The man disappeared after he was rescuing a boy from drowning.
• The underlined part is he was rescuing a boy from drowning.
• Options: was rescued, has been rescued, had rescued, No improvement.
• The intended meaning is that the man rescued a boy and then disappeared.

Concept / Approach:
To express that one past action happened before another past action, English commonly uses the past perfect tense for the earlier action and the simple past for the later one. In this sentence, the earlier action is rescuing the boy, and the later action is the man disappearing. Therefore, the clause after he had rescued a boy from drowning is the correct form. The other options either change the subject of the verb or use inappropriate tenses that do not fit the time relationship between the events.

Step-by-Step Solution:
Step 1: Identify the two actions: the man disappeared and he rescued a boy from drowning. Step 2: Decide which action happened first. The rescue was completed first, and the disappearance happened after that. Step 3: Apply the rule for sequence of tenses in the past. The earlier action should be in past perfect, and the later action in simple past. Step 4: Transform the earlier action into past perfect: he had rescued a boy from drowning. Step 5: Place this clause after after: The man disappeared after he had rescued a boy from drowning. Step 6: Examine option C, had rescued, which exactly produces this correct structure. Step 7: Reject the other options: was rescued makes the boy the subject, has been rescued introduces present relevance, and No improvement would leave the incorrect was rescuing.

Verification / Alternative check:
Compare the sentence with other standard examples: He left after he had finished the work, She went home after she had completed the exam. In each case the earlier action uses the past perfect. If we say He left after he was finishing the work, the sentence sounds wrong and fails to show that the work was completed before leaving. The structure The man disappeared after he had rescued a boy from drowning fits the same pattern and clearly shows the correct order of events.

Why Other Options Are Wrong:
Was rescued is passive and would mean the man was rescued by someone else, which changes the story completely. Has been rescued is a present perfect passive form and implies ongoing relevance now, which does not fit a narrative about a past event. No improvement retains was rescuing, which suggests that he disappeared while in the middle of the action, but the presence of after implies that the rescue had already been completed, so this tense is inappropriate.

Common Pitfalls:
Many students are unsure about when to use the past perfect and either overuse it or avoid it altogether. A helpful guideline is to reserve the past perfect for situations where you need to emphasise that one past action was completed before another. Time conjunctions such as after, before, and when often trigger this need. In such cases, using had plus past participle for the earlier action, as in had rescued, provides clarity and is favoured in formal written English.

Final Answer:
The correct improvement is had rescued, giving: The man disappeared after he had rescued a boy from drowning.