Let Numerator = x
Denominator = y
Fraction will be xy
A fraction becomes 911, if 2 is added to both the numerator and the denominator.
⇒ (x+2)(y+2)=911
By cross multiplication, we get;
11x + 22 = 9y + 18
Subtracting 22 from both sides, we get
11x = 9y - 4
Dividing by 11, we get,
x=9y−411 … (i)
Given that 3 is added to both the numerator and the denominator it becomes 56.
(x+3)(y+3)=56 … (ii)
By Cross multiplication, we get
6x + 18 = 5y + 15
Substituting the value of x, we get;
6(9y−4)11+18=5y+15
Subtract 18 from both sides, we get;
6(9y−4)11=5y−3
54y−24=55y−33
-y = -9
y = 9
Putting this value of y in equation (i), we get,
x = 9y−411 … (i)
x=(81−4)11
x=7711
x = 7
Hence, our fraction is xy = 79.