Question

The population of the village is 5000. If in a year, the numbers of males were to increase by 5% and that of the female by 3% annually, the population would grow to 5202 at the end of the year. Find the number of males and females in the village.

Answer 1

Hint: In this question, we need to determine the total population of the males as well as the females in the village such that the initial population was 5000. For this, we will establish two mathematical equations according to the conditions given in the question with the variables as the population of the male and the females and then, solve the equations simultaneously.

Complete step-by-step answer:
Let the number of the males in the village be ‘m’ and that of the female be ‘f’.
According to the question, the total initial population of the village was 5000. So,
 $ \Rightarrow m + f = 5000 - - - - (i) $
Also, it has been given that the population of the male increases by 5% and of the female increases by 3% annually. So,
New population of the male is given as $ m + 5\% m = 1.05m $
New population of the female is given as $ f + 3\% m = 1.03f $
According to the question, the new total population is 5202. So,
 $ \Rightarrow 1.05m + 1.03f = 5202 - - - - (ii) $
Solving the equation (i) and (ii) to determine the population of the male and the female.
From the equation (i), we can write
 $ \Rightarrow m = 5000 - f - - - - (iii) $
Substituting the value from the equation (iii) in the equation (ii) we get
 $
\Rightarrow 1.05(5000 - f) + 1.03f = 5202 \\
\Rightarrow 1.05 \times 5000 - 1.05f + 1.03f = 5202 \\
\Rightarrow 5250 - 0.02f = 5202 \\
\Rightarrow 0.02f = 5250 - 5202 \\
\Rightarrow f = \dfrac{{48}}{{0.02}} \\
   = 2400 \\
  $
Hence, the total population of the females in the village is 2400.
Now. Substituting the value of the population of the females in the equation (iii), we get
 $
  m = 5000 - f \\
   = 5000 - 2400 \\
   = 2600 \\
  $
Hence, the total number of males in the village is 2600.
Therefore, we can say that the total number of the males and the females in the village is 2600 and 2400 respectively.

Note: While writing the mathematical equation according to the conditions given in the question, we need to consider all the parameters involved in the question such as here we have only two parameters i.e., population of the males and the females.