Question

The population of Rampur in 1998 was 32000. In 1999 it decreased by 15% and in 2000 increased by 25%. What was the population in the year 2000?
A) 33000
B) 34000
C) 44800
D) 36900

Answer 1

Hint: Population of year 1998 is given, percentage of decrease for the next year is also given, and applying this percentage decrease on the previous population we can calculate the population of the year 1999. Percentage increase for the year 2000 is given, applying this percentage increase on the previous population we can calculate the required population of the year 2000.

Complete step-by-step answer:
The population of Rampur in 1998 was 32000. It is given that in 1999 it decreased by 15%. The population in 1999 becomes:
🡪 $ {P_{1999}} $ = 32000 - 15% of 32000
Calculating the value of this population:
 $
  {P_{1999}} = 32000 - \dfrac{{15}}{{100}} \times 32000 \\
   \Rightarrow {P_{1999}} = 32000 - 4800 \\
   \Rightarrow {P_{1999}} = 27200 \;
  $
Thus population of the town in 1999 was 27200
Now, according to the question, the population increased by 25% in the year 2000. The population in 2000 becomes:
🡪 $ {P_{2000}} $ = \[{P_{1999}}\] + 15% of \[{P_{1999}}\]
Calculating the value of this population:
 $
  {P_{2000}} = 27200 + \dfrac{{25}}{{100}} \times 27200\left( {\because {P_{1999}} = 27200} \right) \\
   \Rightarrow {P_{2000}} = 27200 + 6800 \\
   \Rightarrow {P_{2000}} = 34000 \;
  $
Therefore, the population in the year 2000 of the given town of Rampur was $ 34000 $ and the correct option is B).
So, the correct answer is “Option B”.

Note: We represent the percentage with the symbol ‘%’ and it means ‘part per hundred’. That’s why when percentage is converted to fraction for calculation, the base of the fraction is 100.
For the decrease in population, we use a negative sign and for the increase, a positive sign for the percentage calculation on previous year’s population.