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The present population of the town is 25,000.It grows at 4% ,5% and 8% in the first year ,second year and third year respectively,the population after three years is
A.29484
B.28696
C.24,579
D.30,184
Answer
![Verified]()
Verified
Verified
Hint: Here it is enough if we find the percentage value at the end of each year and add it with the population of the previous year.
Complete step-by-step answer:
Step 1:
We are given that at present the population is 25000.
Let us consider the present population to be ${P_1}$
${P_1} = 25000$
Now it is given that there is a population rise of 4% in the first year .
This is nothing other than 4% of ${P_1}$, people have increased.
So ,let's find the value of 4% of ${P_1}$,
$
\Rightarrow \dfrac{4}{{100}}*25000 = 4*250 \\
{\text{ }} = 1000 \\
$
Therefore there is a rise of 1000 people at the end of first year .
So now the population at the end of first year is ${P_1} + 1000$
Let the new population be${P_2}$
Therefore
$
{P_2} = {P_1} + 1000 = 25000 + 1000 = 26000 \\
\therefore {P_2} = 26000 \\
$
Step 2:
Now let's repeat the same process with ${P_2}$
Now it is given that there is a population rise of 5% in the second year .
This is nothing other than 5% of ${P_2}$, people have increased.
So ,let's find the value of 5% of ${P_2}$,
$
\Rightarrow \dfrac{5}{{100}}*26000 = 5*260 \\
{\text{ }} = 1300 \\
$
Therefore there is a rise of 1300 people at the end of second year when compared to the previous year.
So now the population at the end of second year is ${P_2} + 1300$
Let the new population be${P_3}$
Therefore
$
{P_3} = {P_2} + 1300 = 26000 + 1300 = 27300 \\
\therefore {P_3} = 27300 \\
$
Step 3:
Now let's repeat the same process with ${P_3}$
Now it is given that there is a population rise of 8% in the third year .
This is nothing other than 8% of ${P_3}$, people have increased.
So ,let's find the value of 8% of ${P_3}$,
$
\Rightarrow \dfrac{8}{{100}}*27300 = 8*273 \\
{\text{ }} = 2184 \\
$
Therefore there is a rise of 2184 people at the end of third year when compared to the previous year.
So now the population at the end of third year is ${P_3} + 2184$
Let the new population be${P_4}$
Therefore
$
{P_4} = {P_3} + 2184 = 27300 + 2184 = 29484 \\
\therefore {P_4} = 29484 \\
$
Therefore the population after three years is 29,484.
The correct option is A
Note: The percent rate is calculated by dividing the new value by the original value and multiplying by 100%. The percentage value or new value is calculated by multiplying the original value by the percent rate and dividing by 100%.
Complete step-by-step answer:
Step 1:
We are given that at present the population is 25000.
Let us consider the present population to be ${P_1}$
${P_1} = 25000$
Now it is given that there is a population rise of 4% in the first year .
This is nothing other than 4% of ${P_1}$, people have increased.
So ,let's find the value of 4% of ${P_1}$,
$
\Rightarrow \dfrac{4}{{100}}*25000 = 4*250 \\
{\text{ }} = 1000 \\
$
Therefore there is a rise of 1000 people at the end of first year .
So now the population at the end of first year is ${P_1} + 1000$
Let the new population be${P_2}$
Therefore
$
{P_2} = {P_1} + 1000 = 25000 + 1000 = 26000 \\
\therefore {P_2} = 26000 \\
$
Step 2:
Now let's repeat the same process with ${P_2}$
Now it is given that there is a population rise of 5% in the second year .
This is nothing other than 5% of ${P_2}$, people have increased.
So ,let's find the value of 5% of ${P_2}$,
$
\Rightarrow \dfrac{5}{{100}}*26000 = 5*260 \\
{\text{ }} = 1300 \\
$
Therefore there is a rise of 1300 people at the end of second year when compared to the previous year.
So now the population at the end of second year is ${P_2} + 1300$
Let the new population be${P_3}$
Therefore
$
{P_3} = {P_2} + 1300 = 26000 + 1300 = 27300 \\
\therefore {P_3} = 27300 \\
$
Step 3:
Now let's repeat the same process with ${P_3}$
Now it is given that there is a population rise of 8% in the third year .
This is nothing other than 8% of ${P_3}$, people have increased.
So ,let's find the value of 8% of ${P_3}$,
$
\Rightarrow \dfrac{8}{{100}}*27300 = 8*273 \\
{\text{ }} = 2184 \\
$
Therefore there is a rise of 2184 people at the end of third year when compared to the previous year.
So now the population at the end of third year is ${P_3} + 2184$
Let the new population be${P_4}$
Therefore
$
{P_4} = {P_3} + 2184 = 27300 + 2184 = 29484 \\
\therefore {P_4} = 29484 \\
$
Therefore the population after three years is 29,484.
The correct option is A
Note: The percent rate is calculated by dividing the new value by the original value and multiplying by 100%. The percentage value or new value is calculated by multiplying the original value by the percent rate and dividing by 100%.
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