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.

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.

             

Let        Numerator   = x

Denominator  = y

Fraction will              = x/ y

A fraction becomes 9/11, if 2 is added to both the numerator and the denominator

(x+2)   =          9

 y+2               11

Cross multiply we get

11 x + 22        = 9y + 18

Subtract 22 both side we get

11 x     = 9 y – 4

Divide by 11 we get

 x        = 9 y – 4     

                                                            11                          … (1)

Given that 3 is added to both the numerator and the denominator it becomes 5/ 6.

If, 3 is added to both the numerator and the denominator it becomes 5/6

(x+3)   =          5                      … (2)

 y+3                6

Cross multiply we get

 6x + 18 = 5y + 15

 Subtract the value of x now we get

    6(9 y – 4 )   + 18 = 5y + 15

                                      11                  

Subtract 18 both side we get

 6(9 y – 4 )     = 5y  - 3 

                                    11                   

                       

54   – 24         =  55 y  -  33

-y         =  -9

y         = 9

Plug this value of y in equation (1)  we get

x               = 9 y – 4     

11                                … (1)

x          = (81 – 4)/77

x          = 77/11

x          = 7

Hence our fraction is 7/9