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

Appeared in: RRB Staff Nurse Mumbai-2015

Explanation

The problem requires finding the ratio A : B from the equation 15% of A = 20% of B.
This equation can be written as 15A = 20B after removing the common factor of 1/100 from both sides.
Rearranging the terms to find A/B gives A/B = 20/15.
Simplifying the fraction 20/15 by dividing both numerator and denominator by 5 results in 4/3.
Therefore, the ratio A : B is 4 : 3.

Option A: This is the inverse ratio B : A, not A : B. It results from incorrectly setting up the ratio as 15 : 20 instead of 20 : 15.
Option C: This ratio is unrelated to the calculation. It may arise from misinterpreting the percentages or performing incorrect arithmetic operations, such as adding or subtracting the numbers.
Option D: Similar to option C, this ratio is not derived from the given information. It's likely included as a random distractor.

Visual 1: Infographic: A step-by-step visual guide showing how to convert 'x% of A = y% of B' into the ratio A : B = y : x.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving ratio and proportion problems involving percentages as background academic context rather than a clinical decision trigger.
While this is a math question, understanding ratios and proportions is crucial in nursing for tasks like medication dosage calculations, interpreting lab value ratios (e.g., Albumin/Globulin ratio), and calculating IV drip rates.
For example, if a medication needs to be diluted in a 1:10 ratio, a nurse must accurately calculate the amount of medication and diluent.
What if? If the question was '15% of A is 20 more than B', the equation would be 0.15A = B + 20, which describes a linear relationship, not a direct ratio.

How to Approach the Question

Identify the core task: The question asks for the ratio A : B given an equality involving percentages of A and B.
Translate the words into a mathematical equation: '15% of A = 20% of B' becomes (15/100) * A = (20/100) * B.
Simplify the equation by removing common factors. Here, you can cancel the '/100' on both sides to get 15A = 20B.
Rearrange the equation to match the desired ratio format. To get A : B (or A/B), isolate A on one side and B on the other. This gives A/B = 20/15.
Simplify the resulting fraction to its lowest terms. Divide both 20 and 15 by 5 to get 4/3.
Match the final simplified ratio, 4:3, with the given options.

Concept Tested & Keywords

Q51NbcuZS4n9IUJG1cIGOx

Practise the full RRB Staff Nurse Mumbai-2015

Attempt every question from this paper in a timed mock, then review the full solution for each one.