Question

A shopkeeper buys a number of books of $\text{Rs.}80$. If he had bought $4$ more books for the same amount, each book would have cost $\text{Rs.}1$ less. How many books did he buy?

Answer 1

Let, the number of books bought be $x$.

Then cost of $x$ books $=\text{Rs.}80$

Cost of one book $=\text{Rs.}\frac{80}{x}$

If the number of books bought is $(x+4)$,

then, cost of one book $=Rs.\frac{80}{x+4}$

It is given that the cost of one book is reduced by one rupee.

$\therefore \frac{80}{x}-\frac{80}{x+4}=1$

$80\left[\frac{x+4-x}{x(x+4)}\right]=1$

$\frac{320}{x^2+4x}=1$

$x^2+4x=320$

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

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

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

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

$x=-20$ or $x=16$

Hence the number of books is $16$.