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

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