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प्रश्न
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?
उत्तर
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.
