Quadratic Equations

  • Question
    CBSEENMA10009838

    A shopkeeper buys some books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost Rs. 1 less. Find the number of books he bought.


                                                OR


    The sum of two number is 9 and the sum of their reciprocals is 12. Find the numbers.

    Solution

    Total cost of books = Rs.80

    Let the number of books = x

    So the cost of each book = Rs 80x

    Cost of each book if he buy 4 more books = Rs 80x + 4

    As per given in equations:

     

    80x - 80x + 4 = 1 80x + 320 - 80xx( x + 4) = 1  320x 2+ 4x = 1 x2 + 4x - 320 = 0 (x + 20) ( x- 16) = 0 x = -20   or   x = 16

    Since number of books cannot be negative,

    so the number of books he brought is 16.

     

                                       OR

     

    Let the frist number be x then the second number be 9 - x as the sum of both  number is 9.

    Now the sum of their reciprocal is 12, therefor

     =  1x + 19 - x = 12 9 - x + xx( 9 - x ) = 12 99x - x2 = 12  18= 9x - x2   x2 - 9x + 18 = 0  ( x- 6 ) ( x - 3 ) = 0  x = 6   or   x = 3

    If  x = 6 then other number is 3.

    And, if x = 3 then other number is 6.

    Hence numbers are 3 and 6.

     

     

     

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