Question

The boys and girls in a school are in the ratio \[8:3\]. If the number of girls is \[405\], how many boys are there in the school ?

Answer 1

Hint: We define the ratio of two numbers as the relation between the two numbers. The ratio of two numbers also tells how larger or smaller one number is than the other number. It is simply fraction but in reduced form which is obtained by cancelling out the common factors of both numerator and denominator. We write the equation basically in two ways, first writing two fractions as equal, or by representing this fraction using colon as a:b=c:d. If one of these four numbers is missing, then we can find it by using basic properties of fraction.

Complete step by step solution :
The ratio of number of boys to the number of girls in a school is given as \[8:3\]
Let number of boys be given by ${{n}_{b}}$
And number of girls be ${{n}_{g}}$
Then mathematically
$\dfrac{{{n}_{b}}}{{{n}_{g}}}=\dfrac{8}{3}$
According to the question
Number of girls, \[{{n}_{g}}=405\]
Now we have to find the number of boys
To do this, we put the value of ng in the above equation and then solve for ${{n}_{b}}$
$\dfrac{{{n}_{b}}}{405}=\dfrac{8}{3}$
$
 \Rightarrow \begin{array}{*{35}{l}}
   {{n}_{b}}=405\times 8/3 \\
=135\times 8 \\
\end{array} \\
=1080 \\
$

Thus, there are \[1080\] boys in the school.

Note :
The equation which states two ratios are equal is called proportion. The symbol used for proportion is "::" or "=". Ratio and proportion are important topics not only in the field of mathematics but also in science, business, analytics and many more.