Question

By increasing the list price of a book by ₹12, a person can buy 24 books less for ₹1728. The original price of the book was_____.

• A. ₹24
• B. ₹20
• C. ₹16
• D. ₹18

Answer 1

The correct option is A ₹24

Let the original price of the book be $₹x.$
The increased price of the book will be $₹(x+12).$
The total amount to be spent is $₹1728.$

Number of books which can be purchased in the first case is $\frac{1728}{x}$ and the number of books which can be purchased in the second case is $\frac{1728}{x+12}$.

Given, $\frac{1728}{x}-\frac{1728}{x+12}=24$
$\Rightarrow 1728\times 12=24\times x(x+12)$
$\Rightarrow 2x^2+24x-1728=0$
$\Rightarrow x^2+12x-864=0$

For a quadratic equation $a{x}^2+bx+c$,
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here $a=1,b=12$ and $c=-864$

So, $x=\frac{-12\pm \sqrt{(12{)}^2-4\times 1\times -864}}{2\times 2}$

$x=\frac{-12\pm \sqrt{3600}}{2}=\frac{-12\pm 60}{2}$

$x=24orx=-36$

$x$ cannot be a negative value. So $x=24$

So, the original price of the book = ₹24