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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. - ICSE Class 10 - Mathematics

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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.

  Is there an error in this question or solution?

APPEARS IN

Solution 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.
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