If a bookstore owner buys 15 books less for Tk. 900 when the price of each book goes up by Tk. 3, then find the original price of a book.

Question: If a bookstore owner buys 15 books less for Tk. 900 when the price of each book goes up by Tk. 3, then find the original price of a book.

Solution:
Let the original price of a book be x Tk.
Number of books for Tk. 900 at original price = 900/x.
New price after Tk. 3 increase = (x + 3) Tk.
Number of books for Tk. 900 at new price = 900/(x + 3).

According to the question,
900/x - 900/(x + 3) = 15
⇒ 1/x - 1/(x + 3) = 15/900
⇒ {(x + 3) - x} / {x(x + 3)} = 1/60
⇒ 3 / (x² + 3x) = 1/60
⇒ x² + 3x = 180
⇒ x² + 3x - 180 = 0
⇒ x² + 15x - 12x - 180 = 0
⇒ x(x + 15) - 12(x + 15) = 0
⇒ (x + 15)(x - 12) = 0

Either, x + 15 = 0 ⇒ x = - 15 (Price cannot be negative)
Or, x - 12 = 0 ⇒ x = 12

∴ The original price of a book is 12 Tk.