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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
Original cost of each book
= ₹ x
∴ Number of books for ₹960 = `(960)/x`
Now, if cost of each book = ₹(x - 8)
Number of books for ₹960 = `(960)/(x - 8)`
According to the question
`(960)/x + 4 = (960)/(x - 8)`
or
`(960)/((x - 8)) - (960)/x = 4`
`(960x - 960x + 7,680)/(x (x - 8)) = 4`
or
7,680 = 4x2 - 32x
or
x2 - 8x - 1,920 = 0
x2 + 40x - 48x - 1,920 = 0
x (x + 40) - 48 (x + 40) = 0
(x + 40) (x - 48) = 0
⇒ x = -40, 48
as cost can't be - ve x = 48.
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