Question

A fraction becomes 9/11, if 3 is added to both the numerator and denominator. If 3 is added to both the numerator and denominator it becomes 5/6 as well. So what will be the original fraction?

Answer 1

The original fraction is `27/33`

Explanation:

Let's translate in math expressions:

1) `x/y=9/11`

2) `(x+3)/(y+3)=5/6`

The expression 1) is equivalent to `x=9/11y`

then we will substitute in expression 2) and get:

`(9/11y+3)/(y+3)=5/6`

that is equivalent to the following:

`(9/11y+3)*6=5(y+3)`

Let's expand and get

`54/11y+18=5y+15`

The let's solve the equation and get y:

`54/11y-5y=15-18`

`(54-55)/11y=-3`

`-1/11y=-3`

`y=33`

then we will find x

`x=9/11y=9*33/11=27`

The fraction is `27/33`