Sentence completion: the sentence given below has a blank. Choose the option that best completes the sentence. The two boys ______ each other for the first place.

Introduction / Context:
This question checks your knowledge of the correct verb and preposition combination to describe competition. The sentence talks about two boys competing for the first place, and you must choose the phrase that best fits standard English usage.

Given Data / Assumptions:

• Sentence: The two boys ______ each other for the first place.
• Options: contended for, fought with, vied with, struggled to.
• The idea is organised, perhaps fair, competition for the top position.

Concept / Approach:
The verb vie means to compete eagerly with someone for something. The standard pattern is vie with someone for something. So the natural phrase is vied with each other for the first place. This combines the correct verb, preposition, and object to describe competition between two people.

Step-by-Step Solution:
Step 1: Identify that the key idea is competing for first place, not physical fighting. Step 2: Recall the collocation vie with someone for a prize or position. Step 3: Fit it into the sentence: The two boys vied with each other for the first place. Step 4: Confirm that this sounds idiomatic and grammatically complete.

Verification / Alternative check:
You can check other example sentences: Companies vie with one another for market share, or Teams vie with each other for the championship. These patterns match the structure in the question, proving that vied with is the right choice here.

Why Other Options Are Wrong:

• contended for: The usual structure is contend with someone for something. Contended for each other is not correct; the missing with makes it ungrammatical in this exact sentence.
• fought with: Suggests physical fighting, not organised competition for first place, and the sentence would need fought with each other for first place, which still sounds less precise for examination competition.
• struggled to: Needs an infinitive verb after it, as in struggled to win or struggled to study, so it does not fit directly before each other.

Common Pitfalls:
Candidates sometimes choose contended for because it seems close in meaning to compete for, but they forget the correct preposition pattern. Others pick fought with because they link competition with fighting. Learning common collocations such as vie with for helps avoid such mistakes in exams.

Final Answer:
Correct option: vied with.