Question

Question 10 (i)
The population of a place increased to 54,000 in 2003 at a rate of 5% per annum.
(i) Find the population in 2001.

Answer 1

(i) Here , A2003=Rs 54,000 R = 5% , n=2 years
Population would be less in 2001 than 2003 in two years.
$\therefore A_{2003}=P_{2001}{(1+\frac{R}{100})}^n$
$\Rightarrow 54000=P_{2001}{(1+\frac{5}{100})}^2\Rightarrow 54000=P_{2001}{(1+\frac{1}{20})}^2$
$\Rightarrow 54000=P_{2001}{\left(\frac{21}{20}\right)}^2\Rightarrow 54000=P_{2001}\times \frac{21}{20}\times \frac{21}{20}$
$\Rightarrow P_{2001}=\frac{54000\times 20\times 20\times 20}{21\times 21}$
$\Rightarrow P_{2001}=48,980\left(approx\right)$