Question

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

Answer 1

Let $x$ and $y$ be the price of one book and no. of books respectively.

Therefore,

Total amount spent $=xy$

$\Rightarrow 300=xy.....\left(1\right)$

Now,

Changed price of book $=Rs.(x-5)$

$\Rightarrow$ No. of books bought $=y+5$

Again,

Total amount spent $=(x-5)(y+5)$

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

$325=300+5(x-y)$

$\Rightarrow 5(x-y)=325-300$

$\Rightarrow x-y=\frac{25}{5}=5$

$\Rightarrow y=x-5.....\left(2\right)$

From equation $\left(1\right)\&\left(2\right)$, we have

$x(x-5)=300$

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

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

$\because x\ne -ve(\because \text{Price of book cannot be negative})$

$\therefore x=20$

Hence the actual cost of book is $x=Rs.20$.