Question

The population of a town increased arithmetically from one lakh to 1.5 lakh during a decade. Find the percentage of increase in population per year.

• A. 50%
• B. 5%
• C. 100%
• D. 33%

Answer 1

Answer:

B. 5%

The percentage of increase in population per year is 5%.

1. Identify the Core Values

• Initial Population: 1 Lakh = 1,00,000

• Final Population: 1.5 Lakh = 1,50,000

• Time Period (Decade): 10 years

2. Calculate the Total Increase

Subtract the initial population from the final population:
$1,50,000 - 1,00,000 = 50,000$

3. Calculate the Annual Increase

Because the population increased arithmetically, it means the population grew by a fixed, equal amount each year. Divide the total increase by the 10 years in a decade:
$50,000 \div 10 = 5,000 \text{ people per year}$

4. Find the Annual Percentage Increase

To find the annual rate, divide the yearly increase by the original population, then multiply by 100:
$\left(\frac{5,000}{1,00,000}\right) \times 100 = 5\%$