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Question
If the price of a book is reduced by ₹ 5, a person can buy 4 more books for ₹ 600. Find the original price of the book.
Solution
Let the original price of the book be ₹ x.
∴ Number of books bought at original price for ₹ `600=600/x`
If the price of a book is reduced by ₹ 5, then the new price of the book is ₹ (x-5)
∴ Number of books bought at reduced price for ₹ `600=600/(x-5)`
According to the given condition,
`600/(x-5)-600/x=4`
⇒ `(600x-600x+3000)/(x(x-5))=4`
⇒ `3000/(x^2-5x)=750`
⇒`x^2-5x=750`
⇒`x^2-5x-750=0`
⇒`x^2-30x+25x-750=0`
⇒`x(x-30)+25(x-30)=0`
⇒`x-30=0 or x+25=0`
⇒`x=30 or x=-25`
∴ x=30 (Price cannot be negative)
Hence, the original price of the book is ₹30.
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