Question

A shopkeeper buys a number of books for $₹40$. If he had bought $2$ more books for the same amount, then each book would have cost him $₹1$ less. The number of books he bought is

• A. $10$
• B. $8$
• C. $12$
• D. $16$

Answer 1

The correct option is B $8$

Let the shopkeeper buys $x$ number of books.
According to the question:
Cost of $x$ books $=₹40$
$\therefore$ Cost of each book $=₹\frac{40}{x}$
Again, when he had bought $2$ more books for the same amount then, the cost of each book $=₹\frac{40}{x+2}$
Thus, according to the given condition $\frac{40}{x}-\frac{40}{x+2}=1$
$\Rightarrow \frac{40(x+2)-40x}{x(x+2)}=1$
$\Rightarrow \frac{40x+80-40x}{x(x+2)}=1$
$\Rightarrow 80=x^2+2x$
$\Rightarrow x^2+2x-80=0$
$\Rightarrow x^2+10x-8x-80=0$
$\Rightarrow x(x+10)-8(x+10)=0$
$\Rightarrow (x-8)(x+10)=0$
$\Rightarrow x=8,-10$
Neglecting the negative value, the number of books he bought is $8$.
Hence, the correct answer is option (2).