Question

The Nagar Palika of a certain city start campaign to kill stray dogs, which numbered 1,250 in the city. As a result, the population of stray dogs started decreasing at the rate of \[20\% \] per month. Calculate the number of stray dogs in the city three months after the campaign started.

Answer 1

Hint: Here, we will use the formula to calculate the present population, \[{\text{Population of stray dogs after 3 months = P}} \times {\left( {1 - \dfrac{{\text{R}}}{{100}}} \right)^{\text{T}}}\], where T is the time in years and R is the rate of decrease. Then we will take P is 1,250, R is 20 and T is 2 in the formula to find the required value.

Complete step by step solution: We are given that the population of stray dogs P is 1250, the rate of decrease in population R is \[20\% \] and the time T is 3 months.

Now we will use the formula to calculate the present population, \[{\text{Population of stray dogs after 3 months = P}} \times {\left( {1 - \dfrac{{\text{R}}}{{100}}} \right)^{\text{T}}}\], where T is the time in years and R is the rate of decrease.


Substituting the above values of P, R and T in the above formula, we get
\[
   \Rightarrow {\text{Population of stray dogs after 3 months = 1250}} \times {\left( {1 - \dfrac{{20}}{{100}}} \right)^3} \\
   \Rightarrow {\text{Population of stray dogs after 3 months = 1250}} \times {\left( {\dfrac{{100 - 20}}{{100}}} \right)^3} \\
   \Rightarrow {\text{Population of stray dogs after 3 months = 1250}} \times {\left( {\dfrac{{80}}{{100}}} \right)^3} \\
   \Rightarrow {\text{Population of stray dogs after 3 months = 1250}} \times {\left( {\dfrac{4}{5}} \right)^3} \\
   \Rightarrow {\text{Population of stray dogs after 3 months = 1250}} \times \dfrac{{64}}{{125}} \\
   \Rightarrow {\text{Population of stray dogs after 3 months = 640}} \\
 \]

Hence, the number of dogs in the city is 640.

Note: students use the formula for calculating the present population, \[{\text{Present population = Population }}n{\text{ years ago}} \times {\left( {1 + \dfrac{r}{{100}}} \right)^n}\], where \[n\] is the time in years and \[r\] is the rate of increment, but as there is a decrease in the population not increase, so this formula is wrong here.