In the sentence "I shall be obliged if you could grant me an interview.", the underlined phrase needs to be checked. Choose the option that best improves the underlined part, or select No improvement if the original is already correct and polite.

Introduction / Context:
This sentence improvement question focuses on formal and polite request language in English. The sentence appears to be part of a letter or application in which the writer respectfully asks for an interview. You must decide whether the phrase grant me an interview is appropriate in this formal context or whether one of the alternatives offers a better expression.

Given Data / Assumptions:

• Sentence: I shall be obliged if you could grant me an interview.
• The underlined part is grant me an interview.
• Options: give, allow, permit, No improvement.
• The context is a polite, possibly written, request to a person in authority.

Concept / Approach:
In formal English, grant is a standard verb used when someone in authority gives something requested, such as a favour, permission, or an interview. Phrases such as grant me an interview, grant me leave, or grant my request are highly conventional in formal letters. While give, allow, and permit can also be used in some contexts, grant is the most natural and appropriately formal choice here. Therefore, no improvement is necessary in this part of the sentence.

Step-by-Step Solution:
Step 1: Understand the tone and purpose of the sentence. The writer is making a courteous request and expressing that they would be obliged if the other person agreed. Step 2: Examine the verb grant. It is commonly used when talking about authorities responding to requests, for example, grant a loan, grant a licence, grant a scholarship, or grant an interview. Step 3: Consider give. Although give an interview is possible, grant is more formal and fits better with the phrase I shall be obliged if you could, which signals a very polite tone. Step 4: Consider allow. Allow me an interview is less common and sounds slightly awkward, because allow is typically followed by an infinitive (allow me to do something) rather than a noun like interview. Step 5: Consider permit. Permit me an interview also feels less natural than permit me to attend an interview; the pattern used in the sentence is better served by grant. Step 6: Note that the entire expression I shall be obliged if you could grant me an interview is a conventional and acceptable formal request, so the best answer is No improvement.

Verification / Alternative check:
Look at typical closing lines in application letters or formal requests: I shall be grateful if you kindly grant me an interview, I would be obliged if you could grant me leave for two days. These standard phrases use grant with abstract nouns such as interview or leave. Substituting give, allow, or permit would make the expressions less formal or grammatically awkward. This confirms that grant me an interview is the best form in a formal written context.

Why Other Options Are Wrong:
Give me an interview is understandable but a little informal and does not match the polite, slightly old fashioned style introduced by I shall be obliged. Allow me an interview and permit me an interview do not fit common usage patterns, where allow or permit are usually followed by an infinitive rather than a direct object like interview.

Common Pitfalls:
Candidates sometimes assume that any underlined expression must be incorrect and automatically choose a replacement. However, exam questions frequently include options where the original is the best choice, particularly when it matches standard formal style. To avoid losing marks, always review whether the given phrase is already idiomatic and appropriate in context before deciding to change it.

Final Answer:
The phrase is already correct and suitably formal, so the correct choice is No improvement.