Question

In the library, the ratio of Mathematics books to the Science books is same as the ratio of Science books to History books. If there are $450$ Science books and $300$ History books, then find the number of Mathematics books.

Answer 1

Step $1:$Finding the ratio of Science books to History books:

Ratio of Science books to History books is $\frac{\mathrm{Number}\mathrm{of}\mathrm{science}\mathrm{books}}{\mathrm{Number}\mathrm{of}\mathrm{history}\mathrm{books}}=\frac{450}{300}=\frac{3}{2}=3:2$

Therefore, ratio of Science books to History books is $3:2$

Step $2:$Finding the number of Mathematics books:

Let the number of Mathematics books is $\text{x}$

Therefore the ratio of Mathematics books to the Science books is

$\frac{\mathrm{Number}\mathrm{of}\mathrm{mathematics}\mathrm{books}}{\mathrm{Number}\mathrm{of}\mathrm{science}\mathrm{books}}=\frac{\mathrm{x}}{450}=\mathrm{x}:450$

But we know that, the ratio of Mathematics books to the Science books is same as the ratio of Science books to History books, it means

The ratio of Mathematics books to the Science books is also $3:2$, which means

$$\begin{gathered} \text{⇒x:450=3:2} \\ \text{⇒}\frac{\mathrm{x}}{450}=\frac{3}{2} \\ \Rightarrow \mathrm{x}=\frac{3}{2}\times 450 \\ \Rightarrow \mathrm{x}=675 \end{gathered}$$

Hence, the number of Mathematics books is $675$.