If A = 400 and B = 600, then by what percentage is the value of A less than the value of B?

Introduction / Context:
This question focuses on relative percentage comparison between two numbers. It asks how much one value is less than another in percentage terms. Such comparisons are useful in real situations like salary differences, price changes and performance comparisons. The key is to identify which quantity is taken as the base for the percentage calculation, because the answer changes if you reverse the base.

Given Data / Assumptions:

• Value of A = 400.
• Value of B = 600.
• B is the base quantity since the question asks how much A is less than B.
• We need to compute percentage difference using the formula: (difference / base) * 100.

Concept / Approach:
To find how much A is less than B in percentage, first determine the absolute difference B − A. Then divide this difference by B (because B is the reference) and multiply by 100. This yields the required percentage less. It is important not to mistakenly divide by A, which would answer a different question, namely how much B is more than A.

Step-by-Step Solution:
Step 1: Given A = 400 and B = 600. Step 2: Compute the absolute difference: B − A = 600 − 400 = 200. Step 3: Since we want how much A is less than B, take B as the base. Step 4: Required percentage = (difference / base) * 100 = (200 / 600) * 100. Step 5: Simplify the fraction: 200 / 600 = 1/3. Step 6: Percentage = (1/3) * 100 ≈ 33.33.

Verification / Alternative check:
We can also see that A is two thirds of B, because 400 / 600 = 2/3. So A is missing one third of B. One third as a percentage is 33.33. Therefore, 400 is 33.33% less than 600. The two methods agree, confirming that the answer is correct. This also shows that if something is two thirds of a reference value, it is 33.33% less than that reference value.

Why Other Options Are Wrong:

• 50 would mean the difference is half of B, but 200 is not half of 600.
• 66.66 would arise if someone took 400 as base and wrongly computed how much B is more than A instead of how much A is less than B.
• 25 would correspond to a difference equal to one quarter of B, but 200 is not one quarter of 600.

Common Pitfalls:
A common error is confusing which quantity should be used as base in the percentage formula. Students sometimes compute (600 − 400) / 400 * 100 and obtain 50, which is actually the percentage by which B is greater than A. Another pitfall is rounding early or forgetting that 1/3 corresponds to 33.33 and not 33 exactly. Always read the wording of the question carefully to decide the correct base quantity, and only then apply the percentage formula.

Final Answer:
A is 33.33% less than B.