#### Question

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

#### Solution

Let the original cost of each book = Rs. x

∴ Number of books brought for Rs. 960 = `960/x`

In 2nd case:

The cost of each book = Rs. (x – 8)

A number of books bought for Rs. 960 = `960/(x - 8)`

From the given information, we have:

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

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

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

`=> x^2 - 8x = 1920`

`=> x^2 - 8x - 1920 = 0`

`=> x^2 - 48x + 40x - 1920 = 0`

`=> x(x - 48) + 40(x - 48) = 0`

`=> x = 48 or x = -40`

But x cannot be negative.

∴ x = 48

Thus, the original cost of each book is Rs. 48.