Identity with mutual percentages:\nShow that (A% of B + B% of A) is equal to which of the following?

Introduction / Context:
This question checks comfort with symbolic percentages and distributive reasoning. Recognizing symmetrical expressions helps in algebraic simplification.

Given Data / Assumptions:

• We interpret A% of B as (A/100) * B, and B% of A as (B/100) * A.
• We need the simplified sum in familiar percentage form.

Concept / Approach:
Write both terms explicitly and factor common pieces. Because multiplication is commutative, A * B and B * A are the same. Combine like terms to reach a compact result.

Step-by-Step Solution:

Verification / Alternative check:
Use numbers: Let A = 10 and B = 50. Then A% of B = 10% of 50 = 5; B% of A = 50% of 10 = 5; total = 10. Meanwhile, 2% of AB = 2% of 500 = 10 — matches.

Why Other Options Are Wrong:

• A% of B or B% of A alone accounts for only half the sum.
• “AB% of 3” is not a meaningful standard expression.
• A% of A + B% of B is unrelated to the symmetric cross terms here.

Common Pitfalls:
Confusing “A% of B + B% of A” with “(A+B)% of (A+B)”. Keep symbols aligned with their operands.

Final Answer:
2% of AB