Question

The population of a town increases by $5\%$ annually. If it is $15435$ now, its population $2$ years ago was:

• A. $14000$
• B. $15000$
• C. $13000$
• D. $10620$

Answer 1

The correct option is A $14000$

$Populationnow\left(p\right)=15435$

$Letpopulation1yearagobe=P_1$

$since,populationofatownincreasesby5\%annually$

$\Rightarrow \frac{p_1+\left(p_1\times 5\right)}{100}=p$

$\Rightarrow \frac{p_1+\left(p_1\times 5\right)}{100}=15435$

$\Rightarrow \frac{\left(p_1\times 105\right)}{100}=15435$

$\Rightarrow p_1=\frac{\left(15435\times 100\right)}{105}$

$\Rightarrow p_1=14700$

$Nowsimilarly,$

$Letpopulation2yearagobe=p_2$

$since,populationofatownincreasesby5\%annually$

$\Rightarrow \frac{p_2+\left(p_2\times 5\right)}{100}=p_1$

$\Rightarrow \frac{p_2+\left(p_2\times 5\right)}{100}=14700$

$\Rightarrow \frac{\left(p_2\times 105\right)}{100}=14700$

$\Rightarrow p_2=\frac{\left(14700\times 100\right)}{105}$

$\Rightarrow p_2=14000$

$Hence,$

$thepopulationof2yearagowas14000$

So, option $A$ is correct answer.