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?

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Solution

## Step 1 - Finding the total number of students Let the total students be $x$Number of girls $=60%$of the total number of students $⇒18=60%$ of $x$ $⇒18=\frac{60}{100}×x\left(\because ofmeansmultiplication\right)\phantom{\rule{0ex}{0ex}}⇒18=\frac{60x}{100}\phantom{\rule{0ex}{0ex}}⇒18=\frac{6x}{10}\phantom{\rule{0ex}{0ex}}⇒x=\frac{18×10}{6}\phantom{\rule{0ex}{0ex}}⇒x=3×10\phantom{\rule{0ex}{0ex}}⇒x=30\phantom{\rule{0ex}{0ex}}$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$$\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}\phantom{\rule{0ex}{0ex}}=\frac{3}{2}$Hence, the required ratio is $3:2$

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