Question

In a village, the number of female is greater than the number of males by 31500. If the ratio of the number of females and males is 8:5, find the number of females and males

Answer 1

$\begin{gathered}\begin{gathered}\bf \:Given - \begin{cases} &\sf{Number_{(females)} - Number_{(males)} = 31500} \\ &\sf{Number_{(females)}:Number_{(males)} = 8:5 } \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:To\:find - \begin{cases} &\sf{Number_{(females)} \: and \: Number_{(males)}}  \end{cases}\end{gathered}\end{gathered}$

Basic Concept Used :-

Writing Systems of Linear Equations from Word Problem.

Step :- 1 Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

Step :- 2 Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

Step :- 3 Carry out the plan and solve the problem.

$\large\underline{\bold{Solution-}}$

Given that

• Number of females to the number of males are in the ratio 8 : 5.

So,

$\begin{gathered}\begin{gathered}\bf \: Let \: \begin{cases} &\sf{Number_{(females)} \: = \: 8x} \\ &\sf{Number_{(males)} \: = \: 5x} \end{cases}\end{gathered}\end{gathered}$

Further,

It is given that

• The number of female is greater than the number of males by 31500.

$\rm :\longmapsto\:Number_{(females)} - Number_{(males)} = 31500$

$\rm :\longmapsto\:8x - 5x = 31500$

$\rm :\longmapsto\:3x = 31500$

$\bf\implies \:x = 10500$

$\begin{gathered}\begin{gathered}\bf \: Hence - \: \begin{cases} &\sf{Number_{(females)} \: = \: 8x = 84000} \\ &\sf{Number_{(males)} \: = \: 5x = 52500} \end{cases}\end{gathered}\end{gathered}$