Question

A shopkeeper buys a certain number of books for Rs 960. If the cost per book was Rs 8 less, the number of books that could be bought for Rs 960 would be 4 more. Taking the original cost of each book to be Rs x, write an equation in x and solve it to find the original cost of each book.

Answer 1

Let original cost = Rs x
No. of books bought = `(960)/x`
New cost of books = Rs (x – 8)

∴ No. of books bought = `(960)/(x - 8)`

If no. of books bought is 4 more then cost = `(960)/x + 4`
∴ According to conditions,

`(960)/(x - 8) - (960)/x` = 4

⇒ `960((1)/(x - 8) - (1)/x)` = 4

⇒ `(x - (x - 8))/(x(x - 8)) = (4)/(960)`

⇒ `(x - x + 8)/(x^2 - 8x) = (4)/(960)`

⇒ `(8)/(x^2 - 8x) = (1)/(960)`

⇒ x² - 8x = 8 x 240
⇒ x² - 8x - 1920 = 0

x = `(-(-8)±sqrt((-8)^2 -4(1)(-1920)))/(2)`

= `(8±sqrt(64 + 7680))/(2)`

= `(8 ±sqrt(7744))/(2)`

= `(8 ± 88)/(2)`

= `(8 + 88)/(2), (8 - 88)/(2)`

= `(96)/(2), (-80)/(2)`

= 48, -40 ...(rejecting)
∴ cost of book = ₹48.