Question

the population of a village grows by r% every year the population increases from 10000 to 11025 then r is​

Answer 1

Step-by-step explanation:

rate = 5 %.

by using the formula

p=P(1+R/100)^T

Answer 2

The value of r = 5

Correct question : The population of a village grows by r% every year. In 2 years the population increases from 10000 to 11025. Then r is.

Given :

• The population of a village grows by r% every year.

• In 2 years the population increases from 10000 to 11025.

To find :

The value of r

Formula Used :

If Present population is P and Rate of increase in population is r% per annum then Population after n years

$\displaystyle \sf { A = P \: {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: \: }$

Solution :

Step 1 of 2 :

Form the equation to find the value of r

Initial population = P = 10000

Population after 2 years = A = 11025

Rate of increase in population = r%

Number of years = 2

By the given condition

$\displaystyle \sf { A = P \: {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: \: }$

$\displaystyle \sf{ \implies }11025 = 10000 \times \: {\bigg[1 + \dfrac{r}{100} \bigg]}^{2}$

Step 2 of 2 :

Calculate the value of r

$\displaystyle \sf 11025 = 10000 \times \: {\bigg[1 + \dfrac{r}{100} \bigg]}^{2}$

$\displaystyle \sf{ \implies } {\bigg[1 + \dfrac{r}{100} \bigg]}^{2} = \frac{11025}{10000}$

$\displaystyle \sf{ \implies } {\bigg[1 + \dfrac{r}{100} \bigg]}^{2} = {\bigg[ \frac{105}{100} \bigg] }^{2}$

$\displaystyle \sf{ \implies } {\bigg[1 + \dfrac{r}{100} \bigg]}^{2} = {\bigg[ 1 + \frac{5}{100} \bigg] }^{2}$

$\displaystyle \sf{ \implies } {\bigg[1 + \dfrac{r}{100} \bigg]}^{} = {\bigg[ 1 + \frac{5}{100} \bigg] }^{}$

$\displaystyle \sf{ \implies } \dfrac{r}{100} = \frac{5}{100}$

$\displaystyle \sf{ \implies }r = 5$

Hence the required value of r = 5

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ Population of a town is 9000. If the males by 8%. and the females increase by 5%.the population will be 9600. Then the

https://brainly.in/question/38911833

2. A caravan depreciates in value by 15% each year. two years ago malcolm bought a new caravan costing £24000. what is its ...

https://brainly.in/question/56254095

#SPJ2