Question

In a library, 50% of the total number of books is of Marathi. The books of English are `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 in the library be x

50% of total number of books is of Marathi.

Number of Marathi books = 50% of x

= `(50/100)x`

= `x/2`

The books of English are `(1/3)` of Marathi books.

Number of books of English = `(1/3) xx (x/2)`

= `x/6`

The books on Mathematics are 25% of the English books.

Number of books of Mathematics

= 25% of `x/6`

= `(25/100) xx (x/6)`

= `x/24`

Since there are 560 books of other subjects, the total number of books in the library are

`x = x/2 + x/6 + x/24 + 560`

∴ `x = (x xx 12)/(2 xx 12) + (x xx 4)/(6 xx 4) + x/24 + 560`

∴ ` x = (12x)/24 + (4x)/24 + x/24 + 560`

∴ `x = (12x + 4x + x)/24 + 560`

∴ `x = (17x)/24 + 560`

∴ `x xx 24 = (17x)/24 xx 24 + 560 xx 24`

∴ 24x = 17x + 13440

∴ 24x − 17x = 13440 

∴ 7x = 13440

∴ x = `13440/7`

∴ x = 1920

∴ The total number of books in the library are 1920.