Two numbers are 20% and 50% more than a third number. The second is what percent of the first?

Introduction / Context:This compares two quantities each defined relative to a common third quantity. Using a convenient base for the third number simplifies percentage comparisons.

Given Data / Assumptions:

• Let the third number be T.
• First number F = T * 1.20.
• Second number S = T * 1.50.
• Find S as a percent of F: (S/F) * 100.

Concept / Approach:Because both are scaled from the same base, T cancels out in the ratio S/F. Compute (1.50 / 1.20) * 100 to get the required percentage.

Step-by-Step Solution:S/F = (1.50T) / (1.20T) = 1.50 / 1.20 = 15/12 = 5/4Percentage = (5/4) * 100 = 125%

Verification / Alternative check:Assume T = 100. Then F = 120, S = 150. S as percent of F = (150/120)*100 = 125%.

Why Other Options Are Wrong:90%, 80%, 75%, 120% reflect using the wrong base or arithmetic errors; the exact ratio is 5:4.

Common Pitfalls:Confusing “percent more than third” with “percent of the first”. Always form the requested ratio explicitly.

Final Answer:125%