Percentage equivalence: If 15% of A equals 20% of B, then 25% of A is equal to what percent of B?

Introduction / Context:
This problem tests equivalence transformations with percentages and proportional reasoning. When two different percentages of two quantities are equal, we can form a ratio between the quantities and then translate another percentage accordingly.

Given Data / Assumptions:

• 0.15 * A = 0.20 * B.
• We need 25% of A expressed as a percent of B.
• All quantities are positive real numbers; percentage arithmetic uses base 100.

Concept / Approach:
From 0.15A = 0.20B, divide both sides by 0.15B to get A/B = 0.20/0.15. Once A/B is known, compute (25% of A) as a fraction of B and convert to a percentage. Scaling by a constant preserves ratios.

Step-by-Step Solution:
0.15A = 0.20B ⇒ A/B = 0.20/0.15 = 20/15 = 4/325% of A = 0.25A = (0.25 * A/B) * B0.25 * (A/B) = 0.25 * (4/3) = 1/3Therefore, 25% of A = (1/3) * B = 33 1/3% of B

Verification / Alternative check:
Pick convenient numbers: let B = 3, then A = 4 (from A/B = 4/3). 25% of A = 1. That is 1/3 of B = 33 1/3%, confirming the result.

Why Other Options Are Wrong:
30% and 35% arise from arithmetic slips; 25% assumes A = B; 40% overstates the ratio beyond 4/3 scaling by 0.25.

Common Pitfalls:
Mixing “percent of A” with “percent of B”. Always convert to a common base (here, B) before stating the final percentage.

Final Answer:
33 1/3%