Question

The population of the town was 1,60,000 three years ago. If it has increased by 3% ,2.5% and 5% respectively, in the last three years then what is the present population ?
A.166366
B.177366
C.166377
D.177377

Answer 1

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:
We are given that the population before three years is 160000.
Let us consider that population to be ${P_1}$
${P_1} = 160000$
Now it is given that there is a population rise of 3% in the first year .
This is nothing other than 3% of ${P_1}$, people have increased.
So ,let's find the value of 3% of ${P_1}$,
$
   \Rightarrow \dfrac{3}{{100}}*160000 = 3*1600 \\
  {\text{ }} = 4800 \\
$
Therefore there is a rise of 4800 people at the end of first year .
So now the population at the end of first year is ${P_1} + 4800$
Let the new population be${P_2}$
Therefore
 $
  {P_2} = {P_1} + 4800 = 160000 + 4800 = 164800 \\
  \therefore {P_2} = 164800 \\
$
Step 2:
Now let's repeat the same process with ${P_2}$
Now it is given that there is a population rise of 2.5% in the second year .
This is nothing other than 2.5% of ${P_2}$, people have increased.
So ,let's find the value of 2.5% of ${P_2}$,
$
   \Rightarrow \dfrac{{2.5}}{{100}}*164800 = 2.5*1648 \\
  {\text{ }} = 4120 \\
$
Therefore there is a rise of 4120 people at the end of second year when compared to the previous year.
So now the population at the end of second year is ${P_2} + 4120$
Let the new population be ${P_3}$
Therefore
 $
  {P_3} = {P_2} + 4120 = 164800 + 4120 = 168920 \\
  \therefore {P_3} = 168920 \\
$
Step 3:
Now let's repeat the same process with ${P_3}$
Now it is given that there is a population rise of 5% in the third year .
This is nothing other than 5% of ${P_3}$, people have increased.
So ,let's find the value of 5% of ${P_3}$,
$
   \Rightarrow \dfrac{5}{{100}}*168920 = 0.5*16892 \\
  {\text{ }} = 8446 \\
$
Therefore there is a rise of 84460 people at the end of third year when compared to the previous year.
So now the population at the end of third year is ${P_3} + 8446$
Let the new population be${P_4}$
Therefore
 $
  {P_4} = {P_3} + 8446 = 168920 + 8446 = 177366 \\
  \therefore {P_4} = 177366 \\
$
Therefor the present population is 177366
The correct option is B.

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%.