  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?

Solution

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 = $\frac{1}{3}×\frac{x}{2}=\frac{x}{6}$ Books on mathematics are 25% of the English books = $\frac{25}{100}×\frac{x}{6}=\frac{x}{24}$ Remaining books = 560 So,  $\frac{x}{2}+\frac{x}{6}+\frac{x}{24}+560=x\phantom{\rule{0ex}{0ex}}⇒\frac{17x}{24}+560=x\phantom{\rule{0ex}{0ex}}⇒x-\frac{17x}{24}=560\phantom{\rule{0ex}{0ex}}⇒\frac{7x}{24}=560\phantom{\rule{0ex}{0ex}}⇒x=\frac{560×24}{7}=1920$ Total books in the library are 1920.  MathematicsMathematics - SolutionsStandard VIII

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