Question

A shopkeeper buys some books for $Rs.80.$ If he had bought $4$ more books for the same amount, each book would have cost $Rs.1$ less. Find the number of books he bought.

Answer 1

Let the number of books bought by the shopkeeper be $x.$

Price of $x$ books $=Rs.80$

$\Rightarrow$ Price of 1 book = $\frac{80}{x}$--- (1)

Now, if the number of books had been $(x+4)$

Price of $x+4$ books $=80$

$\Rightarrow$ Price of 1 book=$\frac{80}{x+4}$--- (2)

Now, according to the question, equation (1) - (2) $=1.$

i.e., $\frac{80}{x}-\frac{80}{x+4}=1\Rightarrow \frac{320}{x^2+4x}=1$

$x^2+4x-320=0$

$\Rightarrow x^2+20x-16x-320=0$

$\Rightarrow x(x+20)-16(x+20)=0$

$\Rightarrow (x-16)(x+20)=0$

$\Rightarrow x=16orx=-20$. But number of books can never be $-ve.$

Therefore number of books he bought $=16.$