Grammar improvement: choose the correct form of the sentence Both of us had a different opinion about it.

Introduction / Context:
In many competitive examinations, a very common grammar task is to improve the underlined part of a sentence so that subject verb agreement, pronoun choice, and overall logic are all correct. The sentence here is Both of us had a different opinion about it, and we must select the best version that expresses the idea that the two people did not share the same view.

Given Data / Assumptions:

The subject phrase is Both of us, which refers to two specific people including the speaker.
The sentence needs to show that each person held a separate or distinct opinion, not a single shared one.
We must preserve the past tense meaning and the basic idea about differing opinions.

Concept / Approach:
The key grammar concepts are subject verb agreement and the correct use of distributive expressions. When we want to emphasise that two people have separate or different opinions, the expression Each of us is more precise than Both of us, because each clearly points to individual, separate positions. The verb had is the correct past tense form for both Both of us and Each of us. We also need to keep the phrase a different opinion about it to preserve the core meaning of the sentence.

Step-by-Step Solution:
Step 1: Identify the subject of the sentence, which is Both of us meaning two people including the speaker. Step 2: Notice that the predicate had a different opinion about it tries to say that the two people did not share the same opinion. Step 3: Recognise that the phrase Both of us had a different opinion can sound illogical because both normally suggests togetherness, while a different opinion suggests separateness. Step 4: Replace Both of us with Each of us to highlight individual opinions while keeping the verb had in the past tense. Step 5: Check the final sentence Each of us had a different opinion about it for grammar and clarity.

Verification / Alternative check:
We can quickly test the sentence by rephrasing it: Every one of us had a different opinion about it. This alternative paraphrase is natural and supports the use of Each of us. If we kept Both of us had a different opinion, native usage would more likely be Both of us had different opinions, changing the object to plural. Since the options do not offer that structure, the clearest and grammatically standard choice is the one using Each of us had a different opinion about it.

Why Other Options Are Wrong:
Option A Both of us has a different opinion about it uses has with a plural subject and breaks subject verb agreement, so it is incorrect.
Option C Each of us have a different opinion about it also breaks subject verb agreement, because Each of us takes a singular verb has or had, not have.
Option D No improvement is needed in the sentence is wrong because the original wording is awkward and not the best standard form.
Option E Both of us were having a different opinion about it uses an unnecessary progressive form and the same both plus a different mismatch, which is stylistically poor.

Common Pitfalls:
Learners often use both when they really want to stress separate actions or opinions, where each is better. Another common mistake is to misapply subject verb agreement after expressions like each of us, everyone, or neither of them. These look plural but grammatically behave as singular. Exam setters frequently test this nuance, so it is important to link each to singular verbs such as has or had. Also, candidates may pick No improvement simply because the sentence seems understandable, without checking whether a more standard and precise alternative is available.

Final Answer:
The improved and grammatically correct sentence is Each of us had a different opinion about it.