Question

The population of a man is $180000$, out of which males are \[\dfrac{1}{3}\] of the whole population. Find the number of females. Also, find the ratio of the number of females to the whole population ?

Answer 1

Hint: In this type of question we will use simple algebra. Now, the total number of males + total number of females gives us the total number of population. By using this concept we will get out no. of males and no. of females, by dividing them we will get its ratio.

Step by step solution:
Let no. of females \[ = y\]
Total population = No. of males + no. of females
So, as per the question total no. of population \[ = 180000\]
And population of male
\[\begin{array}{l}
= \dfrac{1}{3} \times 180000\\
 = 60000
\end{array}\]
Hence by putting the value in the question we will get,
\[\begin{array}{c}
180000 = 60000 + y\\
y = 120000
\end{array}\]
So, the total no. of female population is \[120000\].
Now, ratio of the no. of females to the whole population
\[\begin{array}{l}
 = \dfrac{{No.{\text{ }}of{\text{ }}female{\text{ }}population}}{{total{\text{ }}population}}\\
 = \dfrac{{120000}}{{180000}}\\
 = \dfrac{{12}}{{18}}\\
 = \dfrac{2}{3}
\end{array}\]

So, our required ratio is \[\dfrac{2}{3}\].

Note:
We need to take care while applying simple algebra we can also observe population of females as if male population is \[\dfrac{1}{3}\] of whole population so female population must be \[\dfrac{2}{3}\] of whole population and by putting the value we will get our answer. Dimension of ratio is unitless that means ratio has no unit so while taking ratio both numerator as well denominator must be of same unit and if it is not of same unit then first convert it into its favorable dimension and take its ratio