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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.


Solution

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

Total cost $$=$$ Rs. $$960$$.

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

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

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

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

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

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

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

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

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

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

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

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

$$x-48=0$$ 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. $$48$$.

Mathematics

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