Question

The ratio of the number of girls to the number of boys in a class is \[4:3\]. If the number of girls is 8 more than the number of boys, find the total number of boys and girls in the class.

Answer 1

Hint: To solve this question, first of all we will assume the number of boys and girls to be x and y respectively. In this question, we are given the ratio between girls and boys which will make an equation for us to solve. Another equation can be formed by the relation between girls and boys. Now, we get two equations and we have two unknowns, so we can solve the equations easily and find both the unknowns. This will be our required answer.

Complete step-by-step answer:
Now, we are going to solve the complete question.
First of all, we will assume the number of boys in the class be x, and the number of girls in the class be y.
So, we can say that the number of students in the class \[=x+y\]
As stated in the question, the number of girls in the class is 8 more than the number of boys in the class.
So, if we write the same relation in the form of equation, we will get,
\[y=x+8\]
In the question, we are also given the ratio between girls and boys in the class,
Ratio \[=4:3\]
So, the number of girls in the class from the ratio is,
\[=\dfrac{4}{4+3}(x+y)\]
Similarly, the number of boys in the class from the ratio is,
\[=\dfrac{3}{4+3}(x+y)\]
If we solve the equation of number of boys which we got from the ratio, we will get,
\[\begin{align}
 & \Rightarrow \dfrac{3}{4+3}(x+y)=x \\
 & \Rightarrow \dfrac{3}{7}y=x-\dfrac{3}{7}x \\
 & \Rightarrow \dfrac{3}{7}y=\dfrac{4}{7}x \\
 & \Rightarrow 3y=4x \\
\end{align}\]
Now, we got two different simple equations, from which we can find the number of boys and girls in the class.
The two equations are,
\[y=x+8\]
\[3y=4x\]
Now, if we substitute the value of y from the first equation to the second equation, we can easily solve the equations.
So, after substituting the value of y, the equation formed will be,
\[\begin{align}
 &\Rightarrow 3y=4x \\
 &\Rightarrow 3(x+8)=4x \\
 &\Rightarrow 3x+24=4x \\
 &\Rightarrow x=24 \\
\end{align}\]
Hence, the number of boys in the class are 24.
Now, if we put the numerical value of the number of boys in the class in the first equation, we can get the number of girls in the class.
So,
\[\begin{align}
 &\Rightarrow y=x+8 \\
 &\Rightarrow y=24+8 \\
 &\Rightarrow y=32 \\
\end{align}\]
Therefore, the number of girls in the class is 32.

Note: In the process of solving this question we make a lot of equations, but we need only two of them to get the final answer, so choose the equations carefully, as sometimes the wrong pair may make the solution lengthier or may make the complete solution wrong. Also we need to remember that we are finding the number of girls and boys and not the total number of students in the class.