Question

A shopkeeper purchase 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.

Answer 1

Given the original cost of each book be Rs. $x$.

Total cost $=$ Rs. $960$.

$\therefore$ Number of books for Rs. $960=\frac{960}{x}$

If the cost per book was Rs. $8$ less, (i.e., $x-8$) then

Number of books $=\frac{960}{x-8}$

According to equation, $\frac{960}{x-8}=\frac{960}{x}+4$

$\frac{960}{x-8}-\frac{960}{x}=4$

$960\left[\frac{x-x+8}{x(x-8)}\right]=4$

$\frac{8}{x^2-8x}=\frac{1}{240}$

$\Rightarrow x^2-8x=1,920$

$\Rightarrow x^2-8x-1,920=0$

$\Rightarrow x^2-48x+40x-1,920=0$

$\Rightarrow x(x-48)+40(x-48)=0$

$\Rightarrow (x-48)(x+40)=0$

$x-48=0$ or $x+40=0$

$x=48$ or $x=-40$

$\because -40$ is not possible as the cost of a book cannot be negative.
Hence, the original cost of each book $=$ Rs. $48$.