# A Shopkeeper Purchases a Certain Number of Books for Rs. 960. If the Cost per Book Was Rs. 8 Less, the Number of Books that Could Be Purchased for Rs. 960 Would Be 4 More. Write an Equation, Taking the Original Cost of Each Book to Be Rs. X, and Solve It to Find the Original Cost of the Books. - Mathematics

#### Question

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

#### Solution

Let the original cost of each book = Rs. x

∴  Number of books brought for Rs. 960 = 960/x

In 2nd case:

The cost of each book = Rs. (x – 8)

A number of books bought for Rs. 960 = 960/(x - 8)

From the given information, we have:

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

=> (960x - 960 xx 960 xx 8)/(x(x - 8)) = 4

=> x(x- 8) = (960 xx 8)/4

=> x^2 - 8x = 1920

=> x^2 - 8x - 1920 = 0

=> x^2 - 48x + 40x - 1920 = 0

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

=> x = 48 or x = -40

But x cannot be negative.

∴ x = 48

Thus, the original cost of each book is Rs. 48.

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A Shopkeeper Purchases a Certain Number of Books for Rs. 960. If the Cost per Book Was Rs. 8 Less, the Number of Books that Could Be Purchased for Rs. 960 Would Be 4 More. Write an Equation, Taking the Original Cost of Each Book to Be Rs. X, and Solve It to Find the Original Cost of the Books. Concept: Quadratic Equations.