Question

The population of a place increased to $54000$ in $2003$ at a rate of $5\%$ per annum. Its population in $2005$ will be $P$. What is the sum of the digits in $P$

Answer 1

Let $p=$ Initial population $=54000$, i.e., in the year $2003$
Rate of growth $=5\%$
$\therefore$ Population after $2$ years, i.e., in $2005$
$P=p{(1+\frac{R}{100})}^n=54000\times {(1+\frac{5}{100})}^2$
$P=54000\times \frac{105}{100}\times \frac{105}{100}=59535$

$\therefore$ sum of digits in $P=5+9+5+3+5=27$