Question

The list price of a book is reduced by $Rs.5$. a person can buy $5$ more books for $Rs.300$. Find original price.

Answer 1

Let the price of a book $=x$

The number of books $=y$

Then, According to given question,

$xy=300$

$y=\frac{300}{x}$ ……. (1)

Now, price reduced by $5$ and number of books increased by $5$

Then,

$(x-5)(y+5)=300$

$xy-5y+5x-25=300$

Put the value of y by equation (1) to (2) and we get,

$\begin{align}

$x\frac{300}{x}-5\left(\frac{300}{x}\right)+5x-25=300$

$300-5\left(\frac{300}{x}\right)+5x-25=300$

$5x-5\left(\frac{300}{x}\right)-25=0$

$5[x-\left(\frac{300}{x}\right)-5]=0$

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

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

$ {{x}^{2}}-

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

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

If $x-20=0$ then, $x=20$

If $x+15=0$ then, $x=-15$

Now $x=20$ is positive. Then put the value in equation (1)

$\begin{align}

$y=\frac{300}{x}$

$y=\frac{300}{20}$

$y=15$

Then, the price of a book is $x=20Rs.$

And number of books are $y=15$