Question

When the list price of a book is increased by Rs. 10, a person can buy 10 books less for Rs. 1200. The original price of the book was ______.

• A. Rs. 40
• B. Rs. 100
• C. Rs. 30
• D. Rs. 24

Answer 1

The correct option is C

Rs. 30

Let the original price of the book be Rs. x.
The increased price of the book will be Rs. (x + 10).
The total amount to be spent is Rs. 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 $\frac{1200}{x+10}$.

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

Rejecting the negative value, the original price is Rs. 30