Percentage relation between two numbers: 48% of the first number equals 60% of the second number. Determine the ratio of the first number to the second number, keeping percentages and comparative meaning exactly as stated.

Introduction / Context:
This problem tests translation of percentage statements into algebra and then simplifying to a ratio. When one percentage of a quantity equals another percentage of a different quantity, setting up an equation and simplifying is the most reliable method.

Given Data / Assumptions:

• Let the first number be A.
• Let the second number be B.
• Statement: 48% of A equals 60% of B.
• We assume A and B are positive real numbers (typical in ratio questions).

Concept / Approach:
Convert each percentage to a decimal multiplier. Then form an equation 0.48A = 0.60B and isolate A/B (or B/A). Ratios are scale-free, so any common factors can be canceled cleanly without needing actual values of A or B.

Step-by-Step Solution:

Verification / Alternative check:
Pick B = 4 ⇒ A = 5. Check 48% of 5 = 2.4, 60% of 4 = 2.4, which match exactly. Hence the ratio is correct.

Why Other Options Are Wrong:

• 4 : 7 and 3 : 4: Do not satisfy 0.48A = 0.60B upon substitution.
• Could not be determined: The equation uniquely determines the ratio; no ambiguity exists.

Common Pitfalls:
Swapping the percentages or inverting the ratio. A common error is writing 48/60 instead of 60/48 for A/B. Always solve the equation carefully.

Final Answer: