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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 becomes5/6. 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) / y+2  =   9/11

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
6
(x+3 )/ y + 3 = 5/6   --------- (2)
Cross multiply we get
6x + 18 = 5y + 15
Subtract the value of x now we get
6(9 y – 4 )/11   + 18 = 5y + 15
Subtract 18 both side we get
6(9 y – 4 )/11 = 5y  - 3
54   – 24         =  55 y  -  33
-y =  -9
y  = 9
Plug this value of y in equation (1)  we get
x = 9 y – 4 / 11   
x  = (81 – 4)/77
x  = 77/11
x  = 7
Hence our fraction is 7/9        
                                


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