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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.
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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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