one over eight of the books in a library are tamil books and five out of twenty-four of them are chinese books. seven eight of the remaining

one over eight of the books in a library are tamil books and five out of twenty-four of them are chinese books. seven eight of the remaining books are English books.There are 840 english books.Find the total number of books in the library.

Good question.  Let's look at this.

$${\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{24}}}} = {\frac{{\mathtt{1}}}{{\mathtt{3}}}} = {\mathtt{0.333\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

So one third are either Tamil or chinese.  So 2/3 are not.

7/8 of 2/3 are English books

$${\frac{{\mathtt{7}}}{{\mathtt{8}}}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right) = {\frac{{\mathtt{7}}}{{\mathtt{12}}}} = {\mathtt{0.583\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

So 7/12 of total is 840 English books

$$\frac{7}{12}T=840\\\\
T=840\times \frac{12}{7}\\\\
T=1440$$

There are 1440 books in the library