Question

Sanvi purchased some books for Rs. 120. If she purchased 3 more books
for the same amount each book would have cost her Rs. 2 less. Find the
number of books purchased by Sanvi and the price of each book.​

Answer 1

Step-by-step explanation:

Let the no. of books purchased be x.

Price of book = ₹ 120 / x

According to given,

₹ 120/(x+3) = ₹ 120/x - ₹ 2

₹120/(x+3) = (₹120 - ₹2x)/x

₹120 × x = (₹120 - ₹2x) (x+3)

₹120x = ₹120x - ₹2x² + ₹360 - ₹6x

120x - 120x = -2x² - 6x + 360

0 = -2x² - 6x² + 360

-2( x² + 3x - 180 ) = 0

x² + 3x - 180 = 0/-2 = 0

x² + 15x - 12x - 180 = 0

x( x+15 ) -12 ( x+15 ) = 0

(x+15) (x-12) = 0

x + 15 = 0 OR x - 12 = 0

x = -15 OR x = 12

As x = No. of books, is a natural number, x > 0.

x = 12 books

Price of book = ₹120/x = ₹120/12 = ₹10

Ans :

No. of books = 12

Price of a book = ₹10