The population of a town increased from 1,75,000 to 2,26,500 in a decade. The average percent increase of population per year is?

Appeared in: NCL (MP) Nursing Officer - 2019

Explanation

The question asks for the average percent increase per year, which is most straightforwardly calculated using a simple average method.
First, find the total increase in population over the decade. Assuming the final population is 2,62,500, the increase is: 2,62,500 - 1,75,000 = 87,500.
Next, calculate the total percentage increase relative to the initial population: (87,500 / 1,75,000) × 100 = 50%.
Finally, to find the average annual increase, divide the total percentage increase by the number of years: 50% / 10 years = 5% per year.

Option A: This value is incorrect. It appears to be closer to the result of a different calculation method, the Compound Annual Growth Rate (CAGR), which for these numbers is approximately 4.14%.
Option C: This is an incorrect calculation. A 6% simple average increase per year would result in a 60% total increase over 10 years, leading to a final population of 1,75,000 * 1.60 = 2,80,000.
Option D: This is a significant overestimation. An 8.75% simple average increase would mean a total increase of 87.5% over the decade, resulting in a final population of 1,75,000 * 1.875 = 3,28,125.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of Average Annual Percentage Growth as background academic context rather than a clinical decision trigger.
Population growth calculations are fundamental in Community Health Nursing for planning and resource allocation.
Nurses and public health officials use this data to forecast the future need for hospital beds, healthcare staff, vaccines, and community health programs.
What if? If the question asked for the compounded annual growth rate (CAGR), the answer would be different. The CAGR formula would yield approximately 4.14%, which is a more accurate measure for financial and biological growth that compounds over time.

How to Approach the Question

First, carefully identify the initial value (1,75,000), the final value (2,62,500), and the time period (10 years). Note that the number in the question stem may be a typo, and working backward from the options can help identify the correct numbers.
The phrase 'average percent increase per year' usually implies a simple average unless 'compounded' is specified.
Calculate the total absolute increase: Final Value - Initial Value.
Convert the total increase into a percentage of the initial value: (Total Increase / Initial Value) × 100.
Divide this total percentage by the number of years to find the simple average annual rate.
Match your result with the given options.

Concept Tested & Keywords

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