If A is six times more than B, then by what percentage is B less than A, expressed as a percentage of A?

Introduction / Context:
Comparisons of quantities using phrases like "times more" and "percent less" often cause confusion. This question tests the understanding of relative comparison from one quantity to another. Here A is described as six times more than B, and we are asked by what percentage B is less than A. The direction of comparison matters a lot, and mixing them up leads to wrong answers even if the numbers are simple.

Given Data / Assumptions:

• A is six times more than B.
• This phrase is interpreted in arithmetic as A = B + 6B = 7B.
• We must find by what percentage B is less than A.
• The percentage must be taken relative to A, because the question asks how much B is less than A.

Concept / Approach:
The core idea is to translate the verbal description into an equation and then compute the percentage difference. If A is seven times B, then B is only a certain fraction of A. The percentage by which B is less than A can be found by taking the difference A - B and expressing it as a fraction of A, then multiplying by 100. This is different from expressing the difference as a percentage of B, which would answer how much A is more than B instead of how much B is less than A.

Step-by-Step Solution:
Interpret "A is six times more than B" as A = B + 6B = 7B.Therefore A = 7B.Difference between A and B is A - B = 7B - B = 6B.We need the percentage difference relative to A, so compute (A - B) / A * 100.Substitute A = 7B: (6B) / (7B) * 100.This simplifies to (6 / 7) * 100 which is approximately 85.71%.Thus B is 85.71% less than A when measured as a percentage of A.

Verification / Alternative check:
Choose a convenient value for B, say B = 100. Then by the given condition, A is six times more than 100, so A = 100 + 6 * 100 = 700. The difference is 700 - 100 = 600. Now find the percentage by which B is less than A. Compute 600 divided by 700, and then multiply by 100: 600 / 700 * 100 = (6 / 7) * 100, which again gives approximately 85.71%. This numeric example confirms the algebraic answer.

Why Other Options Are Wrong:
83.33% arises if someone wrongly treats A as 6B instead of 7B. In that mistaken interpretation, difference over A would be (5B) / (6B), which equals 83.33%, but this does not match the phrase "six times more than".

64.82% and 28.56% are arbitrary values that do not correspond to any standard misinterpretation of the phrase and do not match the ratio between A and B as defined.

Common Pitfalls:
The biggest confusion is between "six times" and "six times more". Many learners read both phrases as A = 6B, but "six times more" mathematically means B plus an additional six times B, that is seven times B. Exam setters sometimes exploit this language issue to test conceptual clarity. It is safer to rewrite such phrases carefully as equations before working with percentages, and always check which quantity is being taken as the base for the percentage calculation.

Final Answer:
B is 85.71% less than A when expressed as a percentage of A.