The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is

### Concept & Formula This question tests the calculation of an average linear growth rate over time. Because it asks for the "average percent increase... per year" (and not compound annual growth rate), we must first find the total percentage growth over the period, and then divide it equally by the number of years. $$ \text{Total \% Increase} = \left( \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \right) \times 100 $$ $$ \text{Average Annual Increase} = \frac{\text{Total \% Increase}}{\text{Number of Years}} $$ ### Step-by-step Solution **Given:** Initial Population = 1,75,000 Final Population = 2,62,500 Time period = 1 decade = 10 years First, find the absolute increase in population: Increase = $2,62,500 - 1,75,000 = 87,500$ Calculate the total percentage increase over the entire decade: $$ \text{Total \% Increase} = \left( \frac{87,500}{1,75,000} \right) \times 100 $$ Simplify the fraction: Notice that $87,500$ is exactly half of $1,75,000$ ($875 \times 2 = 1750$). $$ = \frac{1}{2} \times 100 = 50\% $$ So, the population grew by 50% over 10 years. Calculate the average percent increase per year: $$ \text{Average per year} = \frac{50\%}{10 \text{ years}} = 5\% \text{ per year} $$ ### Exam Strategy & Shortcut Use the **Ratio Method**. Initial : Final = $175000 : 262500$. Cancel common zeros: $175 : 262.5$. Notice these are multiples of 25. Or, even simpler, double both sides to remove decimals: $350 : 525$. Divide by 25: $14 : 21$. Divide by 7: $2 : 3$. A growth from 2 to 3 is a $ \frac{1}{2} $ increase, which is 50%. 50% over 10 years is 5% per year. ### Common Pitfall A very common mistake in advanced aptitude exams is overthinking and attempting to calculate the Compound Annual Growth Rate (CAGR) using the formula $ A = P(1 + r/100)^n $. Unless the term "compound" is explicitly stated, simple average growth is expected. Using CAGR here would unnecessarily complicate the math and not yield any of the given options. ### Final Answer **Therefore, the correct answer is 5%.**