Question

The population of Hyderabad was 68,09,000 in the year 2011.If it increases at the rate of \[4.7%\] per annum. What will be the population at the end of the year 2015?

Answer 1

Hint: The population will increase on a yearly basis. If the first-year population is calculated, then next year's population will be calculated on the basis of the first year & not by the population given as per question itself.

Given: The population at starting of Hyderabad (on year 2011) = 68,09,000
The increasing rate of population = \[4.7%\]per annum
The population will be calculated on a yearly basis separately.

Complete step by step solution:
The population of Hyderabad at 2011 is equal to 68,09,000.
The population of Hyderabad at 2012 is equal to the population of Hyderabad at 2011 plus population rate increment. Similarly, the population of Hyderabad at 2013 will be equal to population at 2012 plus increment of population as per rate. Therefore,

Population of Hyderabad at 2012
\[\begin{align}
  & =6809000+\dfrac{4.7}{100}\times 6809000 \\
 & =7129023 \\
\end{align}\]

Population of Hyderabad at 2013
\[\begin{align}
  & =7129023+\dfrac{4.7}{100}\times 7129023 \\
 & =7464087 \\
\end{align}\]

Population of Hyderabad at 2014
\[\begin{align}
  & =7464087+\dfrac{4.7}{100}\times 7464087 \\
 & =7814899 \\
\end{align}\]
Population of Hyderabad at 2015
\[\begin{align}
  & =7814899+\dfrac{4.7}{100}\times 7814899 \\
 & =8182199 \\
\end{align}\]


Hence, Population in 2015 will be 81,82,199 (Rounded off to nearest decimal)

Note: The population is always calculated on a yearly basis. It is calculated as compound interest is calculated. These types of questions are complicated as the population is calculated separately every year. The population of a given area is defined as the number of people usually living in that area, measured on 1 January in a given year. The source can be the most recent population census(a census is when the population is counted).The natural population change is calculated by births minus deaths and net migration is the number of immigrants (population moving into the country) minus the number of emigrants (population moving out of the country).