Question

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

Answer 1

Step-by-step explanation:

Let the cost of book be Rs x.

So, the number of books that can be purchased= 60/x

When the cost of book is decreased by Rs 1,

The number of books that can be purchased would be 60/(x-1)

now, according to the question

60/(x-1)= 60/x + 5

Multiplying by x(x-1) both sides,

60/(x-1)*x(x-1)=60/x*x(x-1) + 5*x(x-1)

60x= 60*(x-1) + 5x(x-1)

Using the distributive property of multiplication over addition, we get:

60x= 60x-60+5x^2-5x

Rearranging the above equation, we see that

5x^2-5x-60=0 or

x^2-x-12=0

Factorising the above quadratic equation,

(x+3)(x-4)=0

So,

x= -3 & x= 4

x= -3 is not possible, as cost can not be negative.

So, the cost of each book would be Rs 4.

The number of books that can be purchased= 60/4= 15