The denominator of 97% plus a number, the numerator minus the same number, the fraction is equal to 13% 27. What is the number? Urgent!

The denominator of 97% plus a number, the numerator minus the same number, the fraction is equal to 13% 27. What is the number? Urgent!

Let this number be X
（97-x）/(100+x)=13/27
13(100+x)=27(97-x)
1300+13x=2619-27x
13x+27x=2619-1300
40x=1319
x=1319/40

The denominator of 97 out of 103 plus a number, the numerator minus the same number, the fraction is equal to 13 out of 27. What's the number?
Don't worry about the equation. Can you tell me about the process

Because, 13 / 27 = 65 / 135
97 - 65 = 135 - 103 = 32;
So, this is [32]

A fraction of 13 / 27, the numerator plus a number, the denominator minus the same number, into the simplest fraction is 7 / 3, to find this number using arithmetic
Arithmetical methods don't need equations

If the denominator is 7 / 3, the multiple of 3 can only be 27 - (the multiple of 3), and the multiple of 7 can only be 13 + 1 + (the multiple of 7), so this number is one of 8, 15 and 22. 15 is the multiple of 3, so 15

13 out of 27 plus a number, the denominator minus the same number, the result is 7 out of 3, find this number
fast
The formula is the simplest fraction

63 out of 1066? Check it
【（13/27）+（27X/27）】*【27/（27-X）】=7/3