Reverse percentage relationship: If A is 90% of B, then B is what percent of A?

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:

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%