Question

the cost of some book is rs 60. cost of every book is the same. if the bookseller decreases the cost of rs 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

Answer: The cost of each book is Rs.4 and 15 books can be purchased at this cost.

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

Answer 2

Answer:

The cost of each book is Rs.4 and 15 books can be purchased at this cost.

Step-by-step explanation:

As given:

Cost of some books = Rs 60

cost of every book is same

Cost decreased by 1 rupee

No of books increased = 5

Solution:

Let the cost of one book be Rs x.

So, the number of books that can be purchased=$\frac{60}{x}$

AS it is given that cost of one book decreased by one rupee

so price of one book will be x-1

The number of books that can be purchased would be=$\frac{60}{x-1}$

Now, according to the given conditions

$\frac{60}{x-1}$=$\frac{60}{x}+5$

Multiplying by x(x-1) both sides,

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

cancelling out the same terms and it will become

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

Multiplying the terms inside we will get

60x= 60x-60+5x²-5x

Taking 60x from LHS to RHS

it will become

0=60x-60+5x²-5x-60x

this will become

0=5x²-5x-60

or

5x²-5x-60=0

dividing whole equation by 5 it will become

x²-x-12=0

Mid term breaking of the above equation will lead us to

x²-4x+3x-12=0

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

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

either

x-4 =0               or x+3=0

x = 4      or x=-3

as the price 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