Percent-to-ratio conversion: If 10% of A equals 20% of B, express the simplified ratio A : B and explain the proportional reasoning behind the result.

Introduction / Context: Converting a statement about percentages into a direct ratio is a common aptitude task. The goal is to turn a% of A = b% of B into A : B by isolating the variables and reducing to simplest terms.

Given Data / Assumptions:

• 0.10A = 0.20B.
• A, B > 0.

Concept / Approach: Divide both sides by 0.10 (or equivalently compare coefficients) to get A in terms of B, then write the ratio A : B and reduce if necessary.

Step-by-Step Solution:

Verification / Alternative check: Test with B = 1 ⇒ A = 2. Then 10% of A = 0.2; 20% of B = 0.2. Equality holds.

Why Other Options Are Wrong: 1 : 2 reverses the ratio; 5 : 1 and 10 : 1 overstate A relative to B; 4 : 1 is not supported by the given equality.

Common Pitfalls: Mixing up which side to divide by, or comparing 10 and 20 as if they alone define the ratio without accounting for the variables.

Final Answer: 2 : 1