If a number is 50% more than the other, how much per cent is the second number less than the first?

Appeared in: OSSSC Nursing Officer-2023

Explanation

The core concept is calculating a percentage change relative to a new base.
Let the second number be 100. The first number is 50% more, making it 150.
The difference between the numbers is 50 (150 - 100).
To find how much less the second number is than the first, we calculate the percentage with the first number (150) as the base.
The calculation is (Difference / First Number) × 100, which is (50 / 150) × 100.
This simplifies to (1/3) × 100, which equals 33.33...% or 33 1/3%.

Option A: 16 2/3% (or 1/6) is an incorrect calculation. It does not correspond to a common logical error in this specific problem.
Option B: 20% is a common distractor in percentage problems. It's the result of a different percentage increase.
Option D: 502% is an extremely large and incorrect value, likely a typographical error in the option. A common conceptual error is to choose 50%, assuming that percentage increase and decrease are symmetrical, but 502% is not a plausible answer.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Percentage difference and relative change as background academic context rather than a clinical decision trigger.
While not a clinical question, strong quantitative skills are essential for nurses in various tasks.
Nurses use percentage calculations for drug dosage calculations, interpreting lab value changes, assessing burn surface area (Rule of Nines), and understanding nutritional information.
A solid grasp of percentages helps prevent medication errors and allows for accurate patient monitoring and assessment.

How to Approach the Question

First, identify that the question is asking for a reverse percentage change. The base for the percentage is different for the increase and the decrease.
To make the calculation simple, assume a starting number. The number 100 is usually the easiest choice for percentage problems.
Let the 'other' (second) number be 100.
Calculate the 'first' number, which is '50% more than' 100. This is 100 + (50/100)*100 = 150.
Now, determine the difference (150 - 100 = 50) and the new base. The question asks 'less than the first', so the base is the first number (150).
Calculate the final percentage: (Difference / New Base) × 100 = (50 / 150) × 100.

Concept Tested & Keywords

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