The ratio of storybooks to other books in a library is $2:7$. If the total number of story books is $400$, then find the total number of books in the library.

Step$1$: Find the number of other books in the library:

Let the number of other books in the library is $=x$

As given the total number of storybooks is $=400$

So, The ratio of storybooks to other books in a library is$400:x$

As we have the given ration $2:7$

According to the question:

$$\begin{gathered} \Rightarrow \frac{2}{7}=\frac{400}{x} \\ \Rightarrow x=\frac{400\times 7}{2}(Cross-Multiplication) \\ \Rightarrow x=\frac{200\times 2\times 7}{2} \\ \Rightarrow x=1400 \end{gathered}$$

So, the number of other books in the library is $1400$.

Step $2$: Find the total number of books in the library:

Now, the total number of books in the library is: $Numberofstorybooks+Numberofotherbooks=400+1400=1800$

Hence, the total number of books in the library is $1800$.