If A is six times more than B, by what percentage are the value of B and the value of A different? Specifically, by what percentage is B less than A?

Introduction / Context:
This question assesses the relationship between two quantities when one is described as being several times more than the other. The phrase "six times more than" is usually interpreted in aptitude questions as A = B + 6B = 7B. The task is to compute the percentage by which the smaller quantity is less than the larger one. This emphasizes that percentage comparisons depend on which value is taken as the base in the calculation.

Given Data / Assumptions:
A is stated to be six times more than B, interpreted as A = 7B.
B is the smaller quantity, A is the larger quantity.
We must find the percentage by which B is less than A, using A as the base for percentage comparison.
Values are positive real numbers, and percentage calculations use standard definitions.

Concept / Approach:
If we let B = 1 unit, then A = 7 units based on the interpretation A = B + 6B. The difference A - B is 6 units. The percentage by which B is less than A equals (A - B) / A * 100. Substituting A = 7 and B = 1, the required percentage is 6 / 7 * 100. This fraction evaluates to approximately 85.71 percent. Thus B is 85.71 percent less than A. The exact numbers chosen for B do not matter because the ratio between A and B is fixed.

Step-by-Step Solution:
Let B = 1 unit for simplicity. A is six times more than B, so A = B + 6B = 7B. Therefore A = 7 * 1 = 7 units. Difference between A and B = A - B = 7 - 1 = 6 units. We need the percentage by which B is less than A. Required percentage = (difference / A) * 100 = (6 / 7) * 100. Compute (6 / 7) * 100 = 85.71 percent (approximately). Hence, the value of B is 85.71 percent less than the value of A.

Verification / Alternative check:
We can choose a different convenient value for B, for example B = 10. Then A = 10 + 6 * 10 = 70. The difference is 70 - 10 = 60. Percentage by which B is less than A is (60 / 70) * 100 = 6 / 7 * 100 = 85.71 percent. This reproduces the same percentage result, confirming that the chosen base value for B does not affect the final percentage as long as the ratio A : B remains 7 : 1.

Why Other Options Are Wrong:
64.82 percent does not align with the ratio 7 : 1 and typically arises from a different, incorrect interpretation. 83.33 percent corresponds to a difference ratio of 5 / 6, which is not the case here. 28.56 percent is far too small and does not reflect how much larger A is compared to B. Only 85.71 percent matches the exact ratio of the difference to the larger value A in this situation.

Common Pitfalls:
A common error is misinterpreting "six times more than" as merely A = 6B instead of A = 7B, which would change the percentage completely. Another typical mistake is to calculate the percentage difference using B as the base, which would give 600 percent, describing how much more A is than B rather than how much less B is than A. Always read the wording carefully and identify which quantity is the reference base for the percentage calculation.

Final Answer:
The value of B is 85.71 percent less than the value of A.