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 book.
[4 MARKS]

Answer 1

Framing the equation: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Let the original cost of each book be Rs x.
Then,the no.of books = $\frac{960}{x}$
Also, cost of each books = Rs (x-8)
and no. of books =$\frac{960}{x}+4$
Then, $(x-8)$ $(\frac{960}{x}+4)960$
$\Rightarrow (x-8)(960+4x)=960x\Rightarrow 960x+4x^2-7680-32x=960x\Rightarrow 4x^2-32x-7680=0\Rightarrow x^2-8x-1920=0\Rightarrow x^2+40x-48x-1920=0\Rightarrow (x-48)(x+40)=0\Rightarrow x=48,x=-40$
$\therefore$ Original cost of book = Rs 48.