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.

Answer 1

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` 

⇒ x² – 5x = 750 

⇒ x² – 5x – 750 = 0

⇒ x² – 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.