If three-fifth (3/5) of 60% of a number is 36, then what is the number?

Appeared in: OSSSC Nursing Officer-2021

Explanation

The problem is translated into the mathematical equation: (3/5) × (60/100) × x = 36.
The percentage is converted to a fraction (60% = 3/5), simplifying the equation to (3/5) × (3/5) × x = 36.
This further simplifies to (9/25) × x = 36.
Solving for x involves multiplying 36 by the reciprocal of 9/25, which is 25/9.
The calculation x = (36/9) × 25 results in x = 4 × 25, which equals 100.

Option B: If the number were 80, then 60% of 80 is 48. Three-fifths of 48 is (3/5) × 48 = 28.8, which is not 36.
Option C: If the number were 75, then 60% of 75 is 45. Three-fifths of 45 is (3/5) × 45 = 27, which is not 36.
Option D: If the number were 90, then 60% of 90 is 54. Three-fifths of 54 is (3/5) × 54 = 32.4, which is not 36.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving mathematical word problems involving fractions and percentages as background academic context rather than a clinical decision trigger.
While not a direct clinical calculation, the logical reasoning and step-by-step problem-solving skills tested here are essential for nurses in tasks like medication dosage calculation, interpreting lab results, and managing patient care plans.
What if? If the question was 'three-fifth of 50% of a number is 30', the setup would be (3/5) × (50/100) × x = 30, leading to (3/10) × x = 30, so x = 100. The underlying method of translating words to an equation remains the same.

How to Approach the Question

First, identify the unknown value in the word problem and represent it with a variable, such as 'x'.
Carefully translate the words into a mathematical equation. Remember that 'of' typically means multiplication, '%' means per hundred, and 'is' means equals.
Convert percentages into either fractions or decimals to make the calculation easier (e.g., 60% = 60/100 = 3/5).
Simplify the equation by performing the necessary multiplications on the numbers.
Isolate the variable 'x' on one side of the equation to find its value.
Finally, verify your answer by plugging it back into the original problem statement to ensure it holds true.

Concept Tested & Keywords

Concept Tested: Solving mathematical word problems involving fractions and percentages.
Stem keywords: three-fifth, 60%, number, 36
Lead-in keywords: what is the number

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Practise the full OSSSC Nursing Officer-2021

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