Reverse percentage relationship: If A is 90% of B, then B is what percent of A?
Aptitude
Percentage
Difficulty: Easy
Choose an option
Answer
Correct Answer: 111.1%
Explanation
Introduction / Context:This is a classic “reverse percent” problem. Given A as a certain percent of B, we are asked to express B as a percent of A. Such conversions test ratio inversion skills.
Given Data / Assumptions:
- A = 90% of B ⇒ A = 0.9B.
- We want B as a percent of A.
Concept / Approach:From A = 0.9B, isolate B in terms of A. Then convert the resulting factor to a percentage by multiplying by 100.
Step-by-Step Solution:
A = 0.9B ⇒ B = A / 0.9.B/A = 1 / 0.9 = 1.111…As percent: 1.111… * 100% = 111.1% (recurring).Verification / Alternative check:Pick B = 100 for a quick check. Then A = 90. Now B as a percent of A is 100/90 * 100% = 111.1%.
Why Other Options Are Wrong:
- 90% reverses in the wrong direction (that would be A as a percent of B).
- 190%, 120% are unrelated overestimates.
- 101.1% is far too small; the inverse of 0.9 must exceed 1.10.
Common Pitfalls:Directly “adding 10%” or guessing. Always invert the factor correctly: if A = kB, then B = (1/k)A.
Final Answer:111.1%