Question

A file of $400$ sheets of paper is $6cm$ thick. How thick is a file of $150$ sheets.

Answer 1

Let number sheets $=x$

Thickness of file$=y$

A file of $400$ sheets of paper thickness $=6cm$

A file of $150$ sheets of paper thickness $=acm$

As the number of sheets decreases, thickness of file also decreases in the same ratio. It is a case of direct proportion.

We make use of the relation of type $\frac{x_1}{x_2}=\frac{y_1}{y_2}$

$x_1=400;x_2=150;y_1=6;y_2=a$

So,

$\frac{400}{150}=\frac{6}{a}$

$$\begin{gathered} 400\times a=6\times 150 \\ a=\frac{6\times 150}{400} \\ a=\frac{{\displaystyle \stackrel{\stackrel{3}{\cancel{75}}}{\cancel{150}}}\times \cancel{{\displaystyle \stackrel{0.75}{6}}}}{{\displaystyle \underset{\underset{\cancel{8}}{\cancel{200}}}{\cancel{400}}}} \\ a=3\times 0.75 \\ \therefore a=2.25 \end{gathered}$$

Hence the a file of $150$ sheets of paper thickness is $2.25cm$