Question

Amita buys some books for ₹ 1920. If she had bought 4 more books for the same amount each book would cost her ₹ 24 less. How many books did she buy? What was the initial price of one book?

Answer 1

Let the number of books bought by the Amita be x.

Price of x books = ₹ 1920

Price of 1 book = `₹1920/x`  ......(i)

Now, if the number of books had been (x + 4),

Price of x + 4 books = ₹ 1920

Price of 1 book = `₹ 1920/(x + 4)`  ......(ii)

Now, according to the question, Equation (i) - (ii) = 24

i.e., `1920/x − 1920/(x + 4)` = 24

= `(1920 x + 7680 − 1920 x)/(x ( x + 4))` = 24

= `7680/(x^2 + 4^x)` = `24/1`

= 24x² + 96x − 7680

= 24x² + 96x − 7680 = 0

= 24 (x² + 4x − 320) = 0

= x² + 4x − 320 = 0

= x² + 20x − 16x − 320 = 0

= x(x + 20) − 16(x + 20) = 0

= (x + 20) (x − 16) = 0

= x + 20 = 0 or x − 16 = 0

= x ≠ − 20 or x = 16

Number of books bought = 16

Price of each book = `1920/16`

= ₹ 120