Question

The sum of numerator and denominator of a fraction is 12. If 1 is added to both numerator and denominator the fraction becomes 1 upon 2. Find the fraction ?

Answer 1

Original fraction `(11/3)/(25/3)`

Explanation:

Let the numerator be `n`
and let the denominator be `d`

We are told:
[1]`color(white)("XXX")n+d=12`
[2]`color(white)("XXX")2(n+1)=d+1` (adding 1 to the numerator and denominator makes the fraction equivalent to `1/2`)

[1] implies
[3]`color(white)("XXX")d=12-n`

Substituting (from [3]) `12-n` for `d` in [2]
[4]`color(white)("XXX")2(n+1)=12-n+1`

Simplifying [4]
[5]`color(white)("XXX")2n+2=13-n`

Adding `n-2` to both sides
[6]`color(white)("XXX")3n=11`

Dividing both sides of [6] by `3`
[7]`color(white)("XXX")n=11/3`

Substituting `11/3` for `n` in [3]
[8]`color(white)("XXX")d=12-11/3=25/3`

So the initial fraction must be `(11/3)/(25/3)`

This looks ugly, so maybe we should check against the given conditions:
a. `11/3+25/3=36/3=12` ...as required
b. `(11/3+1)/(25/3+1)=(14/3)/(28/3)=14/28=1/2` ...also as required.

Conclusion: not all answers are pretty.