If 15% of A = 20% of B, then A : B = ?

Appeared in: RRB Staff Nurse Ahmedabad-2015

Explanation

The problem requires converting a statement about percentages into a mathematical equation.
The equation is: (15/100) * A = (20/100) * B, which simplifies to 15A = 20B.
To find the ratio A:B, you need to solve for the fraction A/B.
Rearranging the terms gives A/B = 20/15.
Simplifying the fraction by dividing both numerator and denominator by 5 gives 4/3.
Therefore, the ratio A:B is 4:3.

Option A: This ratio represents B:A, not A:B. It is the inverse of the correct answer.
Option C: This ratio does not result from the mathematical simplification of the given equation. It appears to be an arbitrary combination of numbers.
Option D: Similar to the option 17:15, this ratio is mathematically incorrect and cannot be derived from the equation 15A = 20B.

Visual 1: No visual is required for this type of mathematical calculation question.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving for a ratio from an equation involving percentages as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of mathematical reasoning is a fundamental skill for nurses.
Nurses use ratios and percentages daily for tasks such as calculating medication dosages, determining IV drip rates, and interpreting lab results.
For example, a solution might be described as a 5% dextrose solution (5g of dextrose per 100mL of fluid), which is a percentage concept.

How to Approach the Question

First, carefully read the question to understand the relationship between the two quantities, A and B.
Translate the word problem into a mathematical equation. '15% of A' becomes (15/100) * A and '20% of B' becomes (20/100) * B.
Set up the equation: (15/100) * A = (20/100) * B.
Simplify the equation by removing the denominators. In this case, multiply both sides by 100 to get 15A = 20B.
Rearrange the algebraic terms to isolate the desired ratio, A/B. This gives A/B = 20/15.
Simplify the resulting fraction to its lowest terms by finding the greatest common divisor (5) and dividing both the numerator and denominator by it.

Concept Tested & Keywords

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