Question

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

• A. ₹40
• B. ₹100
• C. ₹30
• D. ₹24

Answer 1

The correct option is C ₹30

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 $\frac{1200}{x}$

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

We are given that, $\frac{1200}{x}-\frac{1200}{x+10}=10$
$\Rightarrow 1200\times 10=10\times x(x+10)$
$\Rightarrow x^2+10x-1200=0$
$\Rightarrow x^2+40x-30x-1200=0$
$\Rightarrow x(x+40)-30(x+40)=0$
$\Rightarrow (x+40)(x-30)=0$
$\Rightarrow x=-40,30$

Rejecting the negative value, the original price is ₹30