If the price of a book is reduced by ₹5, a person can buy 4 more books for ₹600. Find the original price of the book.
Let the original price of the book be ₹x.
$\therefore$ Number of books bought at original price for ₹ $600=\frac{600}{x}$
If the price of a book is reduced by ₹5, then the new price of the book is ₹(x − 5).
$\therefore$ Number of books bought at reduced price for ₹ $600=\frac{600}{x-5}$
According to the given condition,
$\frac{600}{x-5}-\frac{600}{x}=4$
$\Rightarrow \frac{600 x-600 x+3000}{x(x-5)}=4$
$\Rightarrow \frac{3000}{x^{2}-5 x}=4$
$\Rightarrow x^{2}-5 x=750$
$\Rightarrow x^{2}-5 x-750=0$
$\Rightarrow x^{2}-30 x+25 x-750=0$
$\Rightarrow x(x-30)+25(x-30)=0$
$\Rightarrow(x-30)(x+25)=0$
$\Rightarrow x-30=0$ or $x+25=0$
$\Rightarrow x=30$ or $x=-25$
∴ x = 30 (Price cannot be negative)
Hence, the original price of the book is ₹30.