The population of a village decreases at the rate of 20% per annum. If its population 2 years ago was 10000, the present population is = ?

14600
26400
37600
46000

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Present Population \\ = P {(\frac{1 - R}{100})}^{n} \\ = 10000 {(\frac{1 - 20}{100})}^{2} \\ = 10000 {(\frac{100 - 20}{100})}^{2} \\ = 10000 {(\frac{80}{100})}^{2} \\ = 10000 {(\frac{4}{5})}^{2} \\ = 10000 \times \frac{16}{25} \\ = 400 \times 16 \\ = 6400 \end{aligned}

$\eqalign{ & {\text{Present Population}} \cr & = {\text{P}}{\left( {\frac{{1 - {\text{R}}}}{{100}}} \right)^n} \cr & = 10000{\left( {\frac{{1 - 20}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{{100 - 20}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{{80}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{4}{5}} \right)^2} \cr & = 10000 \times \frac{{16}}{{25}} \cr & = 400 \times 16 \cr & = 6400 \cr}$