Question

A fraction becomes 9/11 if 3 is added in numerator nd denominator if 6 is adddd to both numerator and denominator it becomes 5/6 find fractiom

Answer 1

Let the fraction is x/y. Then by the given question,
(x+2)/(y+2)=9/11
or, 11x+22=9y+18
or, 11x-9y=18-22
or, 11x-9y=-4
or, 11x=9y-4
or, x=(9y-4)/11
and, (x+3)/(y+3)=5/6
or, 6x+18=5y+15
or, 6x-5y=15-18
or, 6(9y-4)/11-5y=-3
or, (54y-24-55y)11=-3
or, -y-24=-3×11
or, y+24=33
or, y=33-24=9
then, x=(9×9-4)/11
or, x=(81-4)/11
or, x=77/11=7
∴, x=7,y=9 and the fraction is :7/9

Answer 2

here is your answer by Sujeet,
A/q

Let to be numerator x
'"""""""""". denominator y
x+3/y+3=9/11
11x-9y=-6. ----(1)
Again,
x+6/y+6=5/6
6x-5y=-6 ------(2)


solve the equation by elimination method,
11x-9y=-6. *6
6x-5y=-6. *11
--------------
66x-54y=-36
66x-55y=-66
__________
-y=-30
y=30

Now,

putting the value of y in another equation,

6x-5y=-6
6x-5(30)=-6
6x-150=-6
6x=-6+150
6x=144
x=144/6
x=26

required fraction be x/y=26/30.

that's all