Question

A shopkeeper buys a certain number of books for ₹ 960. If the cost per book was ₹ 10 less, the number of books that could be bought for ₹ 960 would be 8 more. Taking the original cost of each book to be ₹ x, find the value of x.

Answer 1

Let the original cost per book be ₹ x.

Number of books `= 960/x`

If the cost per book were ₹ x − 10, then the number of books bought would be:

`960/(x-10)`

Given that this number is 8 more than before:

`960/x +8`

Multiply both sides by x(x − 10):

960x = 960(x − 10) + 8x(x − 10)

960x = 960x − 9600 + 8x² − 80x

8x² − 80x − 9600 = 0

Divide by 8:

x² − 10x − 1200 = 0

(x − 40) (x + 30) = 0

x = 40 or x = −30

Reject the negative value.

The original cost per book is:

₹ 40