student bought some books for Rs60.Had he bought two books less for the same amount the cost of each book would have been one rupee more. find the number of books bought by the student
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Step-by-step explanation:
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The number of books bought by the student is 12.
• Let the number of books bought by the student be x.
• Given,
Total cost of buying x books = Rs. 60
Cost of buying each book = Rs. 60 / x
• If he had bought two books less, the number of books would be (x - 2).
Then, the cost of buying each book at the same amount would be Rs. 60 / (x - 2).
• According to the question,
Rs. 60 / (x -2) = Rs. (60 / x) + Re. 1
=> 60 / (x -2) = {(60 + (1 × x)} / x
=> 60 / (x - 2) = (60 + x) / x
On cross-multiplying,
60 × x = (60 + x) (x -2)
=> 60x = 60x - 120 + x² - 2x
=> 60x - 60x - 120 + x² - 2x = 0
=> - 120 + x² - 2x = 0
=> x² - 2x - 120 = 0
=> x² - 12x + 10x - 120 = 0
=> x (x - 12) + 10 (x - 12) = 0
=> (x - 12) (x + 10) = 0
=> x - 12 = 0 ; x + 10 = 0
=> x = 12 ; x = - 10
• The number of books bought cannot be a negative number, therefore, x = - 10 is discarded.
Hence, the number of books bought = 12.