Percent-to-ratio conversion: If 30% of A equals 20% of B, determine the ratio A : B in simplest form.

Introduction / Context:
Converting percentage statements into ratios is common. Here, 30% of A equals 20% of B. We must express A : B as a simplest whole-number ratio by translating the percentages into decimal multipliers and then simplifying.

Given Data / Assumptions:
30% of A = 20% of B; assume positive values for A and B.

Concept / Approach:
Translate percentages into multipliers: 30% = 0.30 and 20% = 0.20. Equate 0.30*A = 0.20*B and isolate A/B to get the ratio.

Step-by-Step Solution:
0.30 A = 0.20 B. Divide both sides by 0.10 to remove decimals → 3 A = 2 B. Rearrange: A / B = 2 / 3. Therefore, A : B = 2 : 3.

Verification / Alternative check:
Let A = 2 and B = 3. Then 30% of A = 0.6, and 20% of B = 0.6; equal, confirming the ratio.

Why Other Options Are Wrong:

• 1 : 3, 3 : 2, 3 : 1, 5 : 3 do not satisfy 0.30*A = 0.20*B when tested.

Common Pitfalls:
Forgetting to convert percentages correctly or flipping the ratio when isolating A/B. Keep track of which variable is in the numerator.

Final Answer:
2 : 3