Question

a fraction becomes 9/11 if 2 is added to both numerator and denominator.if 3 is added to both numerator and denomintor it becomes 5/6.find the fraction

Answer 1

Hiii friend,


Let the numerator and denominator be X and Y.


Fraction = Numerator/Denominator = X/Y.


According to question,


(X+2)/(Y+2) = 9/11

11(X+2) = 9(Y+2)

11X + 22 = 9Y + 18

11X - 9Y = 18-22

11X - 9Y = -4-------(1)


Again,


(X+3)/(Y+3) = 5/6


6(X+3) = 5(Y+3)

6X + 18 = 5Y + 15

6X -5Y = 15 - 18

6X - 5Y = -3 ----------(2)


From equation (1) we get,


11X - 9Y = -4

11X = -4+9Y

X = -4+9Y/(11)----------(3)


Putting the value of X in equation (2)


6X - 5Y = -3

6 × (-4+9Y/11) - 5Y = -3

-24 + 54Y/11 - 5Y = -3


-24 + 54Y - 55Y = -3 × 11


-Y - 24 = -33

-Y = -33 + 24

-Y = -9

Y = 9


Putting the value of Y in equation (3)


X = -4+9Y/11 => -4 + 9 × 9 /11 = -4 + 81/11 = 77/11

X = 7

Numerator = X = 7


And,


Denominator = Y = 9


Fraction = Numerator/Denominator = 7/9



HOPE IT WILL HELP YOU....... :-)