Question
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 = ?
Answer: Option B
$$\eqalign{
& {\text{Present Population}} \cr
& = {\text{P}}{\left( {\frac{{1 - {\text{R}}}}{{100}}} \right)^n} \cr
& = 10000{\left( {\frac{{1 - 20}}{{100}}} \right)^2} \cr
& = 10000{\left( {\frac{{100 - 20}}{{100}}} \right)^2} \cr
& = 10000{\left( {\frac{{80}}{{100}}} \right)^2} \cr
& = 10000{\left( {\frac{4}{5}} \right)^2} \cr
& = 10000 \times \frac{{16}}{{25}} \cr
& = 400 \times 16 \cr
& = 6400 \cr} $$
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$$\eqalign{
& {\text{Present Population}} \cr
& = {\text{P}}{\left( {\frac{{1 - {\text{R}}}}{{100}}} \right)^n} \cr
& = 10000{\left( {\frac{{1 - 20}}{{100}}} \right)^2} \cr
& = 10000{\left( {\frac{{100 - 20}}{{100}}} \right)^2} \cr
& = 10000{\left( {\frac{{80}}{{100}}} \right)^2} \cr
& = 10000{\left( {\frac{4}{5}} \right)^2} \cr
& = 10000 \times \frac{{16}}{{25}} \cr
& = 400 \times 16 \cr
& = 6400 \cr} $$
Was this answer helpful ?
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