Question

The cost of some books is $60$. Cost of every book is the same. If the book sell decreases the cost of the book by $1$, one gets $5$ books more for the same amount. What is the cost of each book and how many books are purchased?

Answer 1

let the cost of each book be $Rs.x$

and no. of books be $y$

A/c $xy=60---\left(1\right)$

Also

$(x-1)(y+5)=60----\left(2\right)$

Solving $\left(1\right)$ and $\left(2\right)$ eqn we get

$x=\frac{60}{y}⟺(\frac{60}{y}-1)(y+5)=60$

$(60-y)(y+5)=60y$

$60y+300-y^2-5y=60y$

$y^2+5y-300=0$

$y=15y=-20$ neglecting $(y=-20)$

We get no. of books $=15$

cost of each book $=\frac{60}{15}=Rs.4$