Question

In a library, 50% of total number of books is of Marathi. The books of English are $\frac{1}{3}$rd of Marathi books. The books on mathematics are 25% of the English books. The remaining 560 books are of other subjects. What is the total number of books in the library?

Answer 1

Let the total number of books be x.
50% books are in Marathi = $\frac{50}{100}x=\frac{x}{2}$
Books of English = $\frac{1}{3}$rd of Marathi books = $\frac{1}{3}\times \frac{x}{2}=\frac{x}{6}$
Books on mathematics are 25% of the English books = $\frac{25}{100}\times \frac{x}{6}=\frac{x}{24}$
Remaining books = 560
So,
$$\begin{gathered} \frac{x}{2}+\frac{x}{6}+\frac{x}{24}+560=x \\ \Rightarrow \frac{17x}{24}+560=x \\ \Rightarrow x-\frac{{\displaystyle 17x}}{{\displaystyle 24}}=560 \\ \Rightarrow \frac{7x}{24}=560 \\ \Rightarrow x=\frac{560\times 24}{7}=1920 \end{gathered}$$
Total books in the library are 1920.