Question

In a town, where the population is 90,000, the male population is two-thirds the female population. Find the male and female population of the town.

Answer 1

Hint: We can assume the female population as x and then we would get the male population as \[\dfrac{2}{3x}\]. Then, by using the data given in the question, we can find the value of x.

Complete Step-by-Step solution:
Before proceeding to the question we should know the basic addition of fractions. For example, if we have $\dfrac{2}{3}+\dfrac{5}{6}$ then, we should first calculate the LCM of their denominators, we need to calculate LCM of 3, 6 which is 6.
After that we divide the LCM, by the denominators of each term respectively.
$\dfrac{6}{3}=2$ and $\dfrac{6}{6}=1$.
Now we will multiply the numerators of each term respectively by 2 and 1.
$\Rightarrow \dfrac{2}{3}+\dfrac{5}{6}=\dfrac{2\times 2+5\times 1}{6}$
$\Rightarrow \dfrac{9}{6}$
After that, we will reduce it into the simplest form to get the desired result.
$\Rightarrow \dfrac{3}{2}$
Now, let us come to our question. We have a total population of town at 90,000. We have been given that male population is \[\dfrac{2}{3}\] of the female population.
Let, the female population be $x$ and the male population $=\dfrac{2}{3}x$.
The question we have,
$x+\dfrac{2x}{3}=90000$
We get the LCM of the denominators as 3.
First, we will divide the LCM by denominator of each term separately then, we will multiply the required result with the numerator of each term as mentioned in the above example:
$\Rightarrow \dfrac{3x+2x}{3}=90000$
$\Rightarrow 5x=27000$
$\Rightarrow x=\dfrac{27000}{5}$
$\therefore x=54000$
Hence, the female population is 54000.
The male population is given by $\dfrac{2x}{3}$.
Therefore, substitute the value of $x=54000$ in $\dfrac{2x}{3}$
$\Rightarrow \dfrac{2\times 54000}{3}=36000$
Hence, the female population is 54000 and the male population is 36000.

Note: We have an alternate method to solve. If you are provided with options then take any of the options, through options justify the question. If the question got justified then the option will be the correct answer otherwise go for the next option. There is a possibility of error while calculating the sum of fractions so, be careful while doing calculations. After doing all the calculations just cross-check the answer, by substituting the value of answer in the question.