Question

If the price of a book is reduced by $Rs5$, a person can buy $5$ more books for $Rs300$. Find the original list price of the book.

Answer 1

Let the original list price of the book be Rs. $x$

Number of books bought for $Rs.300=\frac{300}{x}$

Reduced list price of the book $=Rs.(x-5)$

Number of books bought for $Rs.300=\frac{300}{x-5}$

it is given that

$\frac{300}{x-5}-\frac{300}{x}=5$

$\Rightarrow \frac{300x-300x+1500}{x(x-5)}=5$

$\Rightarrow \frac{1500}{x^2-5x}=5$

$\Rightarrow x^2-5x=300$

$\Rightarrow x^2-5x-300=0$

$\Rightarrow x^2-20x+15x-300=0$

$\Rightarrow (x-20)(x+15)=0$

$\Rightarrow x=20orx=-15$

List price cannot be negative, so $x=20$

hence, the original list price of the book $=Rs.20$