Question

By increasing the list price of a book by ₹10, a person can buy 20 books less for ₹1200. The original price of the book was_____.

• A. ₹40
• B. ₹20
• C. ₹30
• D. ₹24

Answer 1

Answer: (B)

Let the original price of the book be $₹x.$
The increased price of the book will be $₹(x+10).$
The total amount to be spent is $₹1200.$

Number of books which can be purchased in the first case is $\frac{1200}{x}$ and the number of books which can be purchased in the second case is $\frac{1200}{x+10}$.

Given, $\frac{1200}{x}-\frac{1200}{x+10}=20$
$\Rightarrow 1200\times 10=20\times x(x+10)$
$\Rightarrow 2x^2+20x-1200=0$
$\Rightarrow x^2+10x-600=0$
$\Rightarrow x^2+30x-20x-1200=0$
$\Rightarrow x(x+30)-20(x+30)=0$
$\Rightarrow (x+30)(x-20)=0$
$\Rightarrow x=-30,20$

Rejecting the negative value, the original price of the book is $₹20.$