Question

A picnic is being planned in a school for Class $VII$. Girls are $60\%$ of the total number of students and are$18$ in number. The picnic site is $55km$from the school and the transport company is charging the rate of $Rs12perkm$. The total cost of refreshments will be $Rs4280.$ Find the ratio of the number of girls to the number of boys in the class?

Answer 1

Step 1 - Finding the total number of students

Let the total students be $x$

Number of girls $=60\%$of the total number of students

$\Rightarrow 18=60\%$ of $x$

$$\begin{gathered} \Rightarrow 18=\frac{60}{100}\times x\left(\because ofmeansmultiplication\right) \\ \Rightarrow 18=\frac{60x}{100} \\ \Rightarrow 18=\frac{6x}{10} \\ \Rightarrow x=\frac{18\times 10}{6} \\ \Rightarrow x=3\times 10 \\ \Rightarrow x=30 \end{gathered}$$

The total number of students is $30$

Step 2- Ratio of the number of girls to the number of boys

Now, the number of boys $=$Total number of students $-$number of girls

the number of boys$=30-18$

the number of boys $=12$

$$\begin{gathered} \frac{\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{}\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{g}\mathbf{i}\mathbf{r}\mathbf{l}\mathbf{s}\mathbf{}}{\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{}\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{b}\mathbf{o}\mathbf{y}\mathbf{s}\mathbf{}}=\frac{18}{12} \\ =\frac{3}{2} \end{gathered}$$

Hence, the required ratio is $3:2$