Question

The population of a city is 20,000. If the rate of increase is 25% every year, then the population after 2 years will be.

• A. 30,000
• B. 32,500
• C. 31,250
• D. 33,125

Answer 1

The correct option is C 31,250

$\text{Given: Population, P}=20,000\text{Rate of increase in population,}R=25\%\text{and}\text{Number of years, n}=2$ years

$\text{Let population after 2 years be A.}$

$A=P\times {[1+\frac{R}{100}]}^n=20000\times [1+\frac{25}{100}{]}^2=20000\times [1+\frac{1}{4}{]}^2=20000\times [\frac{5}{4}{]}^2=20000\times \frac{25}{16}=31250$

$\therefore \text{The population after 2 years}=31,250.$