Question

The ratio of male and female in a city is \[7:8\] respectively their percentage of children among males and females is \[25\% \] and \[20\% \] respectively. If the number of adult females is 156800, what is the total population of the city?

Answer 1

Hint:
First, we will find the number of adult females by subtracting the \[20\% \] from the total percent \[100\% \]. Then we will use the probability of any event happening is given by dividing the number of outcomes of that event divided by the total number of events, that is; $P = \dfrac{{{\text{Number of outcomes}}}}{{{\text{Total number of outcomes}}}}$ to find the ratio for females in city. Then we will assume that the total population will be \[p\] and multiply the percent of adult females, population and the probability for the females to find the required value.

Complete step by step solution:
We are given that the ratio of male and female in a city is \[7:8\] respectively their percentage of children among males and females is \[25\% \] and \[20\% \] respectively and also the number of adult females is 156800.
Now we will find the number of adult females by subtracting the \[20\% \] from the total percent \[100\% \], we get
\[
   \Rightarrow \left( {100 - 20} \right)\% \\
   \Rightarrow 80\% \\
 \]
We have that the ratio of females in a city is 8.
Now we will find the total ratio by adding 7 with 8, we get
\[ \Rightarrow 7 + 8 = 15\]
We know that the probability of any event happening is given by dividing the number of outcomes of that event divided by the total number of events, that is; $P = \dfrac{{{\text{Number of outcomes}}}}{{{\text{Total number of outcomes}}}}$.
So, the probability from the above formula for the adult females in the city is \[\dfrac{8}{{15}}\].
Let us assume that the total population is \[p\].
So, we will multiply the percent of adult females, population and the probability for the females, we get
\[
   \Rightarrow p \times \dfrac{{80}}{{100}} \times \dfrac{8}{{15}} \\
   \Rightarrow p \times \dfrac{{32}}{{75}} \\
 \]
Taking the above equation equal to 156800, we get
\[ \Rightarrow 156800 = p \times \dfrac{{32}}{{75}}\]
Multiplying the above equation by \[\dfrac{{75}}{{32}}\] on both sides, we get
\[
   \Rightarrow 156800 \times \dfrac{{75}}{{32}} = p \times \dfrac{{32}}{{75}} \times \dfrac{{75}}{{32}} \\
   \Rightarrow 156800 \times \dfrac{{75}}{{32}} = p \\
   \Rightarrow 4900 \times 75 = p \\
   \Rightarrow 3,67,500 = p \\
   \Rightarrow p = 3,67,500 \\
 \]

Thus, the total population of the city is 3,67,500.

Note:
Students need to know that there is no need to find the number of the male population unless we are asked to compute. We will not take percent of the adult women population as the number of children or not as it is to understand the problem. We have taken the percentage by dividing the number by 100 or else the answer will be wrong.