Question

Population of Delhi increases by \[10\%\] every year. If the current population of Delhi is 1,331,000 then what is the population 3 years ago?
(a) 1000000
(b) 25000
(c) 10000000
(d) 1543200

Answer 1

Hint: For solving this problem we assume that the population of Delhi 3 years ago as \['x'\] and by applying \[10\%\] increase in population every year until present year comes we get the present population of Delhi which is given in question. Then we get the value of \['x'\] which is the population 3 years ago.

Complete step by step answer:
Let us assume that the population of Delhi 3 years ago as \['x'\]
Let us assume that the population of Delhi 2 years ago as \['y'\]
We are given that every year the population will increase \[10\%\] .
So by increasing the population 3 years ago by \[10\%\] we get
 \[\begin{align}
  & \Rightarrow y=x+\dfrac{10}{100}\times x \\
 & \Rightarrow y=\dfrac{11x}{10} \\
\end{align}\]
Now, let us assume that the population of Delhi 1 year ago as \['z'\]
By increasing the population 2 years ago by \[10\%\] we get
 \[\begin{align}
  & \Rightarrow z=y+\dfrac{10}{100}\times y \\
 & \Rightarrow z=\dfrac{11y}{10} \\
\end{align}\]
By substituting value of \['y'\] in above equation we get
 \[\begin{align}
  & \Rightarrow z=\dfrac{11}{10}\left( \dfrac{11x}{10} \right) \\
 & \Rightarrow z=\dfrac{121x}{100} \\
\end{align}\]
Let us assume that the population of Delhi this year as \['p'\]
By increasing the population 1 year ago by \[10\%\] we get
 \[\begin{align}
  & \Rightarrow p=z+\dfrac{10}{100}\times z \\
 & \Rightarrow p=\dfrac{11z}{10} \\
\end{align}\]
We are given the present population is 1,331,000.
By substituting the value of \['z'\] and \['p'\] we get
 \[\begin{align}
  & \Rightarrow 1331000=\dfrac{11}{10}\left( \dfrac{121x}{100} \right) \\
 & \Rightarrow x=\dfrac{1331000\times 1000}{1331} \\
 & \Rightarrow x=1000000 \\
\end{align}\]
Therefore, the population of Delhi 3 years ago is 1000000.

So, the correct answer is “Option a”.

Note: Students will make mistakes in taking the problem. They mentioned that there is an increase of \[10\%\] in every year. So, students consider the reverse is also true as there will be a decrease of \[10\%\] in the population and calculate in reverse method but, it was wrong because it is increasing and decreasing conditions. It will never happen like that. Also, some may consider there will be a total of \[30\%\] increase in 3 years which will also be wrong because the increase of \[10\%\] depends on before the year.