Analyzing Population Change for Highest Percent Rise

The question asks us to identify the city and year where the percentage rise in population from the previous year was the highest, based on the provided population data for cities P, Q, and R from 2014 to 2020.

Understanding Percentage Rise

To find the percentage rise in population, we use the following formula:

\(\text{Percentage Rise} = \frac{(\text{Population in Current Year} - \text{Population in Previous Year})}{\text{Population in Previous Year}} \times 100\)

We need to calculate this percentage change for each city for every year from 2015 to 2020, comparing the population to the respective previous year (e.g., 2015 population vs. 2014 population, 2016 vs. 2015, and so on). We are only interested in the years where there was a 'rise', meaning the current year's population is greater than the previous year's population.

Calculating Year-wise Percentage Rise

Let's calculate the percentage rise for each city in each year from 2015 onwards:

Calculations for 2015 (compared to 2014):

• City P: Population changed from 40 to 45 lakhs. \(\text{Percentage Rise} = \frac{(45 - 40)}{40} \times 100 = \frac{5}{40} \times 100 = \frac{1}{8} \times 100 = 12.5\%\)
• City Q: Population changed from 20 to 30 lakhs. \(\text{Percentage Rise} = \frac{(30 - 20)}{20} \times 100 = \frac{10}{20} \times 100 = \frac{1}{2} \times 100 = 50\%\)
• City R: Population changed from 50 to 40 lakhs. This is a decrease, so no percentage rise.

Calculations for 2016 (compared to 2015):

• City P: Population changed from 45 to 60 lakhs. \(\text{Percentage Rise} = \frac{(60 - 45)}{45} \times 100 = \frac{15}{45} \times 100 = \frac{1}{3} \times 100 \approx 33.33\%\)
• City Q: Population changed from 30 to 50 lakhs. \(\text{Percentage Rise} = \frac{(50 - 30)}{30} \times 100 = \frac{20}{30} \times 100 = \frac{2}{3} \times 100 \approx 66.67\%\)
• City R: Population changed from 40 to 60 lakhs. \(\text{Percentage Rise} = \frac{(60 - 40)}{40} \times 100 = \frac{20}{40} \times 100 = \frac{1}{2} \times 100 = 50\%\)

Calculations for 2017 (compared to 2016):

• City P: Population changed from 60 to 50 lakhs. Decrease.
• City Q: Population changed from 50 to 55 lakhs. \(\text{Percentage Rise} = \frac{(55 - 50)}{50} \times 100 = \frac{5}{50} \times 100 = \frac{1}{10} \times 100 = 10\%\)
• City R: Population changed from 60 to 70 lakhs. \(\text{Percentage Rise} = \frac{(70 - 60)}{60} \times 100 = \frac{10}{60} \times 100 = \frac{1}{6} \times 100 \approx 16.67\%\)

Calculations for 2018 (compared to 2017):

• City P: Population changed from 50 to 70 lakhs. \(\text{Percentage Rise} = \frac{(70 - 50)}{50} \times 100 = \frac{20}{50} \times 100 = \frac{2}{5} \times 100 = 40\%\)
• City Q: Population changed from 55 to 60 lakhs. \(\text{Percentage Rise} = \frac{(60 - 55)}{55} \times 100 = \frac{5}{55} \times 100 = \frac{1}{11} \times 100 \approx 9.09\%\)
• City R: Population changed from 70 to 80 lakhs. \(\text{Percentage Rise} = \frac{(80 - 70)}{70} \times 100 = \frac{10}{70} \times 100 = \frac{1}{7} \times 100 \approx 14.28\%\)

Calculations for 2019 (compared to 2018):

• City P: Population changed from 70 to 65 lakhs. Decrease.
• City Q: Population changed from 60 to 70 lakhs. \(\text{Percentage Rise} = \frac{(70 - 60)}{60} \times 100 = \frac{10}{60} \times 100 = \frac{1}{6} \times 100 \approx 16.67\%\)
• City R: Population changed from 80 to 90 lakhs. \(\text{Percentage Rise} = \frac{(90 - 80)}{80} \times 100 = \frac{10}{80} \times 100 = \frac{1}{8} \times 100 = 12.5\%\)

Calculations for 2020 (compared to 2019):

• City P: Population changed from 65 to 80 lakhs. \(\text{Percentage Rise} = \frac{(80 - 65)}{65} \times 100 = \frac{15}{65} \times 100 = \frac{3}{13} \times 100 \approx 23.08\%\)
• City Q: Population changed from 70 to 75 lakhs. \(\text{Percentage Rise} = \frac{(75 - 70)}{70} \times 100 = \frac{5}{70} \times 100 = \frac{1}{14} \times 100 \approx 7.14\%\)
• City R: Population changed from 90 to 100 lakhs. \(\text{Percentage Rise} = \frac{(100 - 90)}{90} \times 100 = \frac{10}{90} \times 100 = \frac{1}{9} \times 100 \approx 11.11\%\)

Summary of Percentage Rises

Let's summarize the percentage rises we calculated:

Identifying the Highest Percentage Rise

Looking at the percentage rises calculated for each city in each year:

• Highest rise for City P: 40% in 2018.
• Highest rise for City Q: approximately 66.67% in 2016.
• Highest rise for City R: 50% in 2016.

Comparing the highest rises for each city (40% for P, ~66.67% for Q, 50% for R), the overall highest percentage rise is approximately 66.67%, which occurred for City Q in the year 2016.

Conclusion on Highest Population Rise

Based on the calculations from the population data table, the highest percentage rise in population from the previous year was for City Q in the year 2016, with an increase of approximately 66.67%.

Revision Table: Population Data Analysis

Additional Information: Population Growth Metrics

Beyond percentage rise, there are other ways to measure population growth:

• Absolute Change: The simple difference between the population in the current year and the previous year (e.g., 50 lakhs - 30 lakhs = 20 lakhs increase for City Q in 2016). This tells you the number of people added, but not how significant that addition is relative to the starting size.
• Growth Rate: Often expressed as a percentage, this is the same as the percentage rise calculation. It standardizes the change relative to the initial population size, making comparisons between entities of different sizes more meaningful.
• Annualized Growth Rate: Used when population data is available for periods longer than a year, this calculates the average annual growth rate over that period.

Analyzing both absolute and percentage changes provides a more complete picture of population dynamics. While City R might have had larger absolute increases in some years (e.g., 90 to 100 lakhs is a 10 lakh increase in 2020), a smaller city like Q having a 66.67% rise (20 lakh increase from 30 lakhs) indicates a much more rapid rate of growth relative to its size in that specific year.