Question

The ratio of boys to girls in a class is $3:4$ . There are $20$ girls in the class . How many are boys?

Answer 1

Given: Ratio of boys and girls in class $=3:4$

Number of girl $=20$

Let number of boy be $=x$

It is written as $boy:girl=3:4$

$x:20:\hspace{0.17em}:3\hspace{0.17em}:4$

First and last term is called extreme terms, that is $x$ and $4$ and $20$ and $3$ is called middle terms.

product of extreme terms = product of middle terms

$$\begin{gathered} 4\times x=20\times 3 \\ x=\frac{20\times 3}{4} \\ x=\frac{{\displaystyle \stackrel{5}{\cancel{20}}\times 3}}{{\displaystyle \underset{1}{\cancel{4}}}} \\ x=3\times 5 \\ \therefore x=15 \end{gathered}$$

Hence the number of boys are $15.$