Question

A village had a population of 25000 three years ago.During the first year second year and the third year the population increase at a rate of 5%,6% and 8% respectively.What is the present population of the village

Answer 1

Present population of the village is 30051

Solution:

Given that village had a population of 25000 three years ago

During the first year second year and the third year the population increase at a rate of 5%, 6% and 8% respectively

To find: present population of the village

The present population is given by formula:

$\text { present population }=p\left(1+\frac{x}{100}\right)\left(1+\frac{y}{100}\right)\left(1+\frac{z}{100}\right)$

Where,

p = initial population

x = rate of increase at first year

y = rate of increase at second year

z = rate of increase at third year

Here given that,

x = 5 %

y = 6 %

z = 8 %

p = 25000

Substituting the values we get,

$\begin{aligned}&\text { present population }=25000\left(1+\frac{5}{100}\right)\left(1+\frac{6}{100}\right)\left(1+\frac{8}{100}\right)\\\\&\text { present population }=25000(1.05)(1.06)(1.08)\\\\&\text { present population }=25000 \times 1.20204=30051\end{aligned}$

Thus present population of the village is 30051