Question

40% of the population of a town are men and 39% are women. If the number of children is 12600, find the number of men.

Answer 1

Hint: Assume the total population of the town is ‘x’. Find the percentage of children in the town by subtracting the sum of the percentage of men and women from 100%. Now, find the number of children by using the obtained percentage and equate it with 12600 to find the value of x. Finally, find the value of 40% of x to calculate the number of men.

Complete step-by-step solution
Here, we have been given that in a town there are 40% men and 39% women. The number of children in the town is 12600. We have to find a number of men.
Since, the town contains only men, women and children, therefore we have,
\[\Rightarrow \] Percentage of children = 100% - [percentage of (men + women)]
\[\Rightarrow \] Percentage of children = 100% - (40% + 39%)
\[\Rightarrow \] Percentage of children = 100% - 79%
\[\Rightarrow \] Percentage of children = 21%
\[\Rightarrow \dfrac{\text{Number of children}}{\text{Total population}} \times 100\] = 21
Let us assume the total population of the town is ‘x’. Therefore, we have,
\[\Rightarrow \dfrac{\text{Number of children}}{x} \]= \[\dfrac{21}{100}\]
\[\Rightarrow \] Number of children = \[\dfrac{21x}{100}\] - (1)
Since, we have been given that the total number of children in the town is 12600, therefore substituting this value in the L.H.S of equation (1), we get,
\[\begin{align}
  & \Rightarrow 12600=\dfrac{21x}{100} \\
 & \Rightarrow x=\dfrac{12600\times 100}{21} \\
 & \Rightarrow x=600\times 100 \\
 & \Rightarrow x=60000 \\
\end{align}\]
Hence, the total population of the town is 60000.
Now, we have to determine the number of men in the town.
Since the percentage of men is 40%, so we have,
\[\Rightarrow \dfrac{\text{Number of men}}{\text{Total population}} \times 100 \] = 40
\[\Rightarrow \dfrac{\text{Number of men}}{60000}\] = \[\dfrac{40}{100}\]
\[\Rightarrow \] Number of men = \[\dfrac{40\times 60000}{100}\]
\[\Rightarrow \] Number of men = 24000
Hence, there are 24000 men in the town.

Note: One may note that we must not assume the number of men and women as different variables. It may be confusing. We just have to assume one variable and carry out our calculation using that assumption. Remember that the value of x is not our solution, we have to substitute it in the expression \[\dfrac{40x}{100}\]. Sometimes in a hurry students just write the value of x as an answer. So, the question must be read carefully.