Question

If the 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.

• A. $15$
• B. $20$
• C. $25$
• D. $30$

Answer 1

The correct option is B $20$

Consider the number of books be $y$ and the price of one book be $Rsx$. So, the total amount spent is, $xy=300$.

The changed price of book is $Rs\left(x-5\right)$ and the number of books bought is $\left(y+5\right)$. So, the total amount spent is, $\left(x-5\right)\left(y+5\right)$.

$300=xy+5\left(x-y\right)-25$

$325=300+5\left(x-y\right)$

$25=5\left(x-y\right)$

$y=x-5$

As $xy=300$, then,

$x\left(x-5\right)=300$

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

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

$\left(x-20\right)\left(x+15\right)=0$

$x=20,x=-15$

Since the price cannot be negative, so the original price of the book is $Rs20$.