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 = ?

A. 4600

B. 6400

C. 7600

D. 6000

Answer: Option B

Solution(By Examveda Team)

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