Question

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

Answer 1

Hint:
Each statement of question gives us one equation. the first statement gives us the equation for the difference between the digits and the third statement gives us the equation for the sum of the digits only.

Complete step by step solution:
Given that,
1) The ratio of males and females in a city is 7:8 respectively
2) Their percentage of children among male and female is 25% and 20% respectively
3) number of adult females is 156800
Now the number of adult females is 80% because 20% are children.
Let the total population be p.
Thus, number of adult women \[ = p \times \dfrac{{80}}{{100}} \times \dfrac{8}{{15}}\]
From given data and above equation we can write,
\[
  156800 = p \times \dfrac{{80}}{{100}} \times \dfrac{8}{{15}} \\
   \Rightarrow 156800 = p \times \dfrac{{32}}{{75}} \\
   \Rightarrow p = \dfrac{{156800 \times 75}}{{32}} \\
   \Rightarrow p = 4900 \times 75 \\
   \Rightarrow p = 3,67,500 \\
\]

Thus total populationof he city is 3,67,500.

Note:
1) Students may get confused if they have to take 20% of adult women population as the number of children or not. But that is just a hint or help to proceed with the solution.
2) Here in this problem no need to find the number of the male population, the number of children unless and until asked to find.
3) Whenever you are given ratios or percentages in a problem do take help of it, because it makes your calculations easy.