Question

The population of a city increase 15% annually. if the present population is 20,700,find the population a year ago

Answer 1

Heya !!!

This is your answer.

Given :-

Population of the city -- 20700 .
Increase in population - 15% annually .
Time -- after 1 year.

There are two methods to find it ......

As it is asked only for one year .... so we can use Simple interest formula.....
or we can use Compound intersect Formula too...

I will solve With both methods.....

Using SI formula.....

Let the Total population be Principal ... increase in population....rate ... and time.....

P = 20700.
R = 15%.
T = 1.

$Increase \: in \: population = \frac{p \times r \times t}{100} \\ = \frac{20700 \times 15 \times 1}{100} \\ 207 \times 15 \\ = 3105$
Hence the increase in population is 3105. So population after one year will be 20700 + 3105 = 23805.

Using CI formula .......

$a \: = \: p{(1 + \frac{r }{100} )}^{n}$
Where ...

P is principal.... r is rate of increase and n is no. years.

$a \: = \: 20700{(1 + \frac{15}{100} )}^{1} \\ = 20700(1 + \frac{3}{20} ) \\ = 20700( \frac{20}{20} + \frac{3}{20} ) \\ = 20700 \times \frac{23}{20} \\ = 1035 \times 23 \\ = 23805$
Hence the population after one year will be 23805.

HOPE IT HELPS.....
#MATHS ARYABHATTA