Question

The ratio of boys to girls in a class is$7:6$. If the number of girls in the class is$24$, find the total number of students in the class.

Answer 1

Hint: Multiply a number or a factor say $x$ in the ratio given such that $7x$ represents number of boys and $6x$ represents number of girls. Number of girls should be equated to $24$, to obtain the value of $x$.

Complete step-by-step solution:
The number of girls in the class is, $G = 24$
The ratio of boys to girls in the class is $7:6$
Let the number of boys be $7x$ in the class.
$B = 7x \cdots \left( 1 \right)$
The number of girls in the class is in the class.
$G = 6x \cdots \left( 2 \right)$
Where, is a factor, which is to be multiplied in boys and girls ratio, to give the actual number of boys and girls

According to question,
The number of girls in the class is given by,
$
\Rightarrow 6x = 24 \\
\Rightarrow x = 4 \\
 $
Therefore, the number of boys in the class is given by,
$
\Rightarrow 7x = 7\left( 4 \right) \\
\Rightarrow 7x = 28 \\
 $
The total number students in the class is given by,
$T = $ Total number of boys in the class + Total number of girls in the class
$T = B + G \cdots \left( 3 \right)$
Putting the value of number of boys and girls in equation (3),
$
 \Rightarrow T = 7x + 6x \\
\Rightarrow T = 28 + 24 \\
\Rightarrow T = 52 \\
 $
Hence, the total number of students in the class is $52$ .

Note:The above problem can also be solved by another method.
Total number of students in the class is,
$
\Rightarrow T = 7x + 6x \\
\Rightarrow T = 13x \\
 $
Ratio of number of girls to the total number of students is $\dfrac{{6x}}{{13x}} = \dfrac{6}{{13}}$
The number of girls can also be written as,
$\dfrac{6}{{13}} \times T = 24 \cdots \left( i \right)$