A fraction becomes 9/11 , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6 . Find the fraction.

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3. Form the pair of linear equations for the following problems and find their solution by substitution    method

(v) A fraction becomes 9/11 , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6 . Find the fraction.

Solution:  

Let be numerator = x

  Let be denominator = y

    Fraction=x/y

 If 2 is added in numerator and denominator to the fraction it becomes = 9/11

     (x+2)/(y+2)=9/11

     11(x+2)=9(y+2)

     11x+22=9y+18

     11x-9y+22-18=0

     11x-9y+4=0---------(1)

 If 3 is added in numerator and denominator to the fraction it becomes = 5/6

    (x+3)/(y+3)=5/6

    6(x+3)=5(y+3)

    6x+18=5y+15

    6x-5y+18-15=0

    6x-5y+3=0---------(2)

  By solving equation (1)

    11x-9y+4=0

    11x+4=9y

    Y=(11x+4)/9----------(3)

 Substitute Y=(11x+4)/9 in equation (3)

    6x-5y+3=0 or 6x-5y=-3

    6x/1-5(11x+4)/9=-3

    54x-55x-20/9=-3

    -x-20/9=-27

    -x=-27+20=-7

    Both sides multiply with –

    X=7

    Substitute x=7 in equation (3)

    Y=11(7)+4/9

    =77+4/9=81/9=9

    Fraction is X/y=7/9

 

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