If the height of person A is 40% less than the height of person B, then by what percentage is B's height greater than A's height?

Introduction / Context:
This problem explores the common concept that percentage increase and percentage decrease between two quantities are not symmetric. If A is 40% less than B, this does not mean that B is 40% more than A. Instead, we must compute B's height relative to A's height and convert this ratio into a percentage increase. Understanding this asymmetry between percentage increase and decrease is very important in quantitative aptitude and real-life applications involving discounts, growth and comparisons.

Given Data / Assumptions:
- A's height is 40% less than B's height.- Let B's height be some convenient reference value.- We need to express how much greater B's height is compared to A's height, in percentage terms.- The answer must be the percentage by which B exceeds A.

Concept / Approach:
If one quantity is k% less than another, say A is 40% less than B, then A = (1 - 0.40) * B = 0.60B. To find how much B is greater than A in percentage terms, we consider the ratio B / A and compute the percentage increase relative to A. This is given by (B - A) / A * 100%. Substituting the values of A in terms of B or vice versa solves the problem. The key is to choose a convenient number for B to simplify arithmetic, such as 100 units.

Step-by-Step Solution:
Step 1: Assume B's height is 100 units (for convenience).Step 2: A's height is 40% less than B's.Step 3: 40% of 100 = 40, so A's height = 100 - 40 = 60 units.Step 4: Now we need to find by what percentage B is taller than A.Step 5: B's height = 100 units, A's height = 60 units.Step 6: Difference in height = B - A = 100 - 60 = 40 units.Step 7: Percentage by which B is greater than A = (Difference / A) * 100%.Step 8: Substitute values: (40 / 60) * 100%.Step 9: Simplify 40 / 60 = 2 / 3 ≈ 0.6666.Step 10: Multiply by 100 to get percentage: 0.6666 * 100% ≈ 66.66%.Therefore, B's height is approximately 66.66% greater than A's height.

Verification / Alternative check:
We can use algebra instead of specific numbers.Let B's height = B units.A's height = 60% of B = 0.60B.Difference = B - 0.60B = 0.40B.Percentage by which B is greater than A = (0.40B / 0.60B) * 100%.Simplify: 0.40B / 0.60B = 4 / 6 = 2 / 3.So the percentage is (2 / 3) * 100% ≈ 66.66%.This matches the value obtained using the assumed heights 100 and 60.

Why Other Options Are Wrong:
- 76.66%: This would correspond to a difference larger than 2/3 of A's height, inconsistent with the 40% decrease relationship.- 96.66%: Almost equal to doubling A's height, which does not match the given reduction from B to A.- 86.66%: Again too large; using this would imply A's height is much smaller relative to B than the 40% less statement indicates.

Common Pitfalls:
- Assuming that if A is 40% less than B, then B is 40% more than A, which is incorrect.- Using A as 100 and then trying to back-calculate B incorrectly.- Confusing percentage differences with absolute differences in units and mixing up denominators.- Rounding errors that lead to answers like 67% instead of the more precise 66.66% given in the options.

Final Answer:
B's height is 66.66% greater than A's height.