Question

A shopkeeper buys a certain number of books for Rs.960. If the cost per book was Rs.8 less, the number of books that could be bought would be 4 more. Write an equation taking the original cost of each book as Rs.x and solve it to find the value the original cost of the books.

Answer 1

Answer:

Rs 48

Step-by-step explanation:

Hi,

Let 'x' be the cost price of 1 book

Given that total books cost Rs 960

Number of books he had bought ,N = 960/x------(1)

Given that if the cost per book was Rs.8 less, the number of books that

could be bought would be 4 more

N + 4 = 960/(x - 8)------(2)

Solving (1) and (2), we get

960/x + 4 = 960/(x - 8)

On simplifying we get

x² - 8x - 1920 = 0

(x - 48)*(x + 40) = 0

x =  48

Hence, Original Cost of each book = Rs 48

Hope, it helps !

Answer 2

Answer:

Step-by-step explanation:

Let the number of book bought by the shopkeeper be x and the cost per book be y.

Then we can write (x * y) = Rs 960

or, xy = 960.------------(i)

If the cost per book was Rs.8 less i.e. (y - 8), then 4 more books could be bought.

i.e. (y - 8) * ((x + 4) = Rs 960.

or, (xy - 8x + 4y - 32) = 960 ------------ (ii)

Putting the value of xy we get,

960 - 8x + 3840/x - 32 = 960

or, 8x² + 32x - 3840 = 0.

or, x² + 4x - 480 = 0

or, x² + 24x - 20x - 480 = 0

or, x(x + 24) - 20(x + 24) = 0

or, x = 20 as it cannot be negative.

Therefore, no.of books purchased = 20.

Cost of each book = 960/20 = Rs 48.