Question

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:
(a) 4.37%
(b) 5%
(c) 6%
(d) 8.75%

Answer 1

Hint: In order to solve such a problem first find the increase of population in 10 years then proceed to find the percentage increase in the population for 10 years compared to the initial population. Then find the percentage increase in population for 1 year by dividing the percentage by 10.

Complete step-by-step answer:

First of all 1 decade =10 years
Given initial population of the town = $1,75,000$
Population of the town after 10 years = $2,62,500$
Let us first find out the total increase in population.
Increase in population in 10 years = new population – old population
$
   \Rightarrow 2,62,500 - 1,75,000 \\
   \Rightarrow 87,500 \\
 $
So population increase in 10 years = 87,500
Now, let us find out the percentage increase in population in 10 years.
Percentage increase \[ = \dfrac{{\left( {{\text{Increased population}}} \right)}}{{\left( {{\text{Old population}}} \right)}} \times 100\]
So percentage increase
$
   = \dfrac{{87,500}}{{1,75,000}} \times 100 \\
   = \dfrac{{100}}{2} \\
   = 50\% \\
 $
Now, as we have the percentage increase in population for 10 years. So, let us find out the percentage increase in population for 1 year.
Percentage increase for 1 year \[ = \dfrac{{{\text{Net percentage increase}}}}{{{\text{Number of years}}}}\]
So, Percentage increase for 1 year
$
   = \dfrac{{50\% }}{{10}} \\
   = 5\% \\
$
Hence, the average percent increase of population per year is 5%.
So, option B is the correct option.

Note: In order to solve such problems where we are just given the final and initial population and average increase is asked we need to consider the problem that the percentage rise in population each year is constant. Students must remember the formula and method of conversion of a quantity into percentage; we need not divide the increase with respect to the initial value.