Question

The population of a place increased to 54,000 in 2003 at a rate of 5% per annum.
(i) Find the population in 2001.
(ii) What would be its population in 2005.
(iii) Write any two effects of high populations.

Answer 1

Hint: For solving this problem we will use the concept of percentage and form our equations as per the given data for getting the correct answer easily.

Complete step-by-step answer:

Given:
Population in 2003 $=54000..........(1)$.
Increase in population every year $=5\%$.
Now, let the population in 2001 is $x$ . Before we proceed, we should know that, what do we mean by a 5% increase.
Let us consider initially we have 100 numbers of pens. Then, 1% of 100 $=\dfrac{1}{100}\times 100=1$.
So, 5% of 100 $=\dfrac{5}{100}\times 100=5$.
If there is a 5% increase in the number of pens then, final number of pens = (Initial number of pens) + (5% of the initial number of pens).
$\Rightarrow $ Final number of pens $=100+5=105$.
Let us consider a number $N$ . Then, $y\%$ of $N$ = $\dfrac{y}{100}\times N$ . If $N$ increases by $y\%$ . Then, $N$ will become $N+\dfrac{y}{100}\times N=N\times \left( 1+\dfrac{y}{100} \right)$.
In our question $y=5$ . Then, $N$ will become $N+\dfrac{y}{100}\times N=N\times \left( 1+\dfrac{5}{100} \right)=N\times 1.05$.
From the above calculation, if any number is increased 5% then, it’s final value will be 1.05 times the initial value. We will use this result directly to solve this question.
We have,
Population in 2001 $=x$.
Then, after a 5% increment population in 2002 $=1.05x$.
Similarly, after a 5% increment, the population in 2003 $=1.05\times \left( 1.05x \right)={{\left( 1.05 \right)}^{2}}x...........(2)$.
Now, equating (1) and (2). Then,
$\begin{align}
  & {{\left( 1.05 \right)}^{2}}x=54000 \\
 & \Rightarrow x=\dfrac{54000}{{{\left( 1.05 \right)}^{2}}}=\dfrac{54000}{1.1025}=48979.59184 \\
 & \Rightarrow x\approx 48980 \\
\end{align}$
Thus, the population in 2001 is 48980 approximately.
Now, as a population in 2003 = 54000 . Then, after a 5% increment, the population in 2004 $=1.05\times 54000=56700$.
Similarly, after a 5% increment, the population in 2005 $=1.05\times 56700=59535$ .
Thus, the population in 2005 is 59535.
Now, the impact of high population is given below:
1. Problem of unemployment.
2. Adverse impact on the environment. For example: if the population is huge then more migration of a large number of people to urban areas with industrialization. This results in air, water and noise pollution in big cities and towns.
3. Per capita income will be reduced.

Note: Here, a student must apply the percentage concept carefully and proceed step by step to find the answer for the question. Moreover, calculations should be carried out carefully so that we can get the correct answer.