Question

the population of students in jalahalli village increased to 54,0000 in year 2003 at the rate of 5% per anum, find the population in the 2001​

Answer 1

Answer:

Population of students in jalahalli village at 2001 = 489796

Step-by-step explanation:

Given :

▪︎Population of students increased of students in jalahalli village in year 2003

= ₹54,0000

▪︎Rate per annum

= 5%

To find :

The population at 2001

Taken :

Let the principal be x

And Principal will be the population of the students at 2001 .

To find the population at 2001 use this formula -:

$\boxed{\sf{A=P{(1+\dfrac{r}{100})}^{n}}}$

Where,

A = Final amount of students

P = Principal

r = Rate

n = number of times interest applied at every time period

The number of times the interest applied at every time period -:

=> 2003-2001

=> 2

Solution :

$:\implies\sf{54,0000=x{\bigg(1+\cancel{\dfrac{5}{100}}\bigg)}^{2}}$

$:\implies\sf{54,0000=x{\bigg(\dfrac{1}{1}+\dfrac{1}{20}\bigg)}^{2}}$

L.C.M. of 1 and 20 is 20 .

$:\implies\sf{54,0000=x{\bigg(\dfrac{20+1}{20}\bigg)}^{2}}$

$:\implies\sf{54,0000=x{\bigg(\dfrac{21}{20}\bigg)}^{2}}$

$:\implies\sf{54,0000=x\bigg(\dfrac{21}{20}\times\dfrac{21}{20}\bigg)}$

$:\implies\sf{54,0000=x\bigg(\dfrac{441}{400}\bigg)}$

$:\implies\sf{54,0000\div\dfrac{441}{400}=x}$

$:\implies\sf{\dfrac{54,0000\times400}{441}=x}$

$:\implies\sf{\cancel{\dfrac{216000000}{441}}=x}$

$:\implies\sf{489795.91\:or\:489796(approx)=x}$

So , the population of students in jalahalli village at 2001 is 489796 .