If 60% of a number is equal to 1/3rd of another number. Find the ratio of the first and second number:

Appeared in: ESIC Nursing Officer 2016 (shift-1)

Explanation

The problem requires setting up an equation where 60% of the first number (x) equals 1/3 of the second number (y).
The statement translates to the equation: (60/100) * x = (1/3) * y.
Simplifying the percentage, (60/100) becomes 3/5. The equation is now (3/5) * x = (1/3) * y.
To find the ratio x:y, we rearrange the equation to solve for x/y.
Multiplying both sides by 5/3 gives: x/y = (1/3) * (5/3) = 5/9.
Therefore, the ratio of the first number to the second number is 5:9.

Option A: This option is incorrect. It may arise from a miscalculation or misunderstanding of how to set up the proportion between the percentage and the fraction.
Option B: This option is incorrect and is the reciprocal of the 1:3 option.
Option C: This is the reciprocal of the correct answer. This common error occurs if the ratio is calculated as y:x (second number to the first number) instead of x:y (first number to the second number).

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

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Ratios and Proportions as background academic context rather than a clinical decision trigger.
While this is a general aptitude question, the underlying skills are crucial in nursing. Proficiency with percentages, fractions, and ratios is essential for accurate drug dosage calculations, IV drip rate settings, and interpreting lab results.
For example, a nurse might need to calculate a dose based on a patient's weight (mg/kg) or prepare a solution of a certain concentration (e.g., a 2% solution), both of which involve similar mathematical principles.
Patient safety is directly linked to numeracy skills. A miscalculation in ratios or percentages when preparing medication can lead to significant underdosing or overdosing, with potentially fatal consequences.

How to Approach the Question

First, carefully read the question and identify the relationship described. Here, it's an equality between a percentage of one number and a fraction of another.
Assign variables to the unknown numbers. Let the first number be 'x' and the second number be 'y'.
Translate the words into a mathematical equation. '60% of x' becomes (60/100)*x, and '1/3rd of y' becomes (1/3)*y. So, (60/100)*x = (1/3)*y.
Simplify any fractions or percentages. (60/100) simplifies to 3/5.
The goal is to find the ratio x:y, which is the same as the fraction x/y. Rearrange the simplified equation to isolate x/y on one side.
To solve (3/5)x = (1/3)y for x/y, multiply both sides by 5/3. This gives x/y = (1/3) * (5/3) = 5/9.

Concept Tested & Keywords

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