In this sentence improvement item, you must choose the version that sounds the most natural in standard English. Original sentence: Let his failure be a lesson to you all.

Introduction / Context:
This question focuses on natural phraseology in English when addressing a group. The sentence aims to say that everyone in the group should learn from his failure. While the original version Let his failure be a lesson to you all is understandable, examinations often prefer more standard wording such as to all of you. Your task is to identify the option that best improves the sentence while keeping the meaning unchanged.

Given Data / Assumptions:

• The main structure Let his failure be a lesson is acceptable.
• The phrase to you all can be improved in formal written English.
• Options provide different ways of referring to the whole group.
• The goal is smooth, grammatically standard, and natural expression.

Concept / Approach:
In formal English, the phrase to all of you is widely used to address every member of a group politely. The expression you all appears more in some dialects of spoken English and is less common in formal exam level writing. Option a, to all of you, maintains the plural reference and improves the stylistic quality of the sentence. Other options either sound awkward or add unnecessary words.

Step-by-Step Solution:
Step 1: Identify the part of the sentence that can be improved, namely to you all. Step 2: Consider the standard phrase to all of you, which is commonly used in speeches and formal writing. Step 3: Check option a, to all of you, and mentally substitute it into the sentence to get Let his failure be a lesson to all of you. Step 4: Evaluate option b, to all you people, which sounds informal and slightly redundant. Step 5: Evaluate option c, to all you, which is incomplete and sounds unnatural. Step 6: Consider option d, No improvement, and recognise that although the original is understandable, examination standards usually choose the smoother alternative. Step 7: Select to all of you as the best and most standard improvement.

Verification / Alternative check:
Test the sentence in a formal context, such as a teacher addressing a class: Let his failure be a lesson to all of you. This version reads smoothly and is typical in textbooks and formal speeches. The alternatives To all you people and To all you sound less polished and are rarely found in high quality written material. This confirms option a as the correct improvement.

Why Other Options Are Wrong:
To all you people adds the word people unnecessarily and gives a slightly informal or even patronising tone. To all you is grammatically incomplete and does not match standard patterns. No improvement is not ideal because a better expression exists and is provided among the options. Examinations generally expect candidates to choose the most correct and natural sounding version available.

Common Pitfalls:
Some candidates leave the sentence unchanged because it feels familiar in casual speech. Others select option b as it appears emphatic, but they overlook the redundancy. To perform well in sentence improvement sections, always look for options that maintain the original meaning but provide greater clarity, formality, and grammatical correctness.

Final Answer:
The improved sentence is Let his failure be a lesson to all of you.