Writing the correct scale notes

Did you ever wonder why musicians say that this scale has one flat or that scale has two sharps? Why both sharps and flats are required when we can write any sharpened note as a flattened note? For example we can write C# as Db.Many of you make a serious mistake while writing scale notes. Let us take the example of G major scale. One can write the notes as G, A, B, C, D, E, F#. While someone else can also write the notes as G, A, B, C, D, E, Gb.
There is a rule for writing scale notes. The rule says that no note name should be repeated unless there is no other way. The third note in F major scale is A. So we have already used the note A. Now the fourth note can be A# or Bb. But as the note name A is used already, we have to write Bb. This rule is applicable to all the scales. There are some scales where you can’t apply this rule anyhow.
There is a very simple way to write the scale notes which automatically follows this rule. Let us take the example of D major.
Since the key is D, write all the natural notes starting from D.
So we have D, E, F, G, A, B, C     (let’s call it raw sequence)
Now apply the formula of major scale: WWHWWWH (W: whole step, H: half step)
The rule: You can only add a sharp or flat to the notes of the raw sequence and cannot change note names.
Now, according to the major scale formula there should be a whole step between D and the next note. This is already satisfied by the note E. So there is no need to add sharp or flat to E.
Now distance between E and next note should be again a whole step. Next note is F and distance between E and F is a half step. So to make it a full step, change F to F#.
Now distance between F# and next note should be half step. This is satisfied by G. Don’t disturb G.
Continue this way, and you will automatically know whether to add a flat or sharp.
Take the scale notes of the major scale in every key and you will find that none of the scales contain both sharps and flats. Either it will have some flatted notes or some sharped notes but never a mixture of both.
Now I am sure that you clearly understand what a musician mean by a flat key or a sharp key.
 

If both ways would have been correct, then the major scale with one sharp would be G major and also the major scale with one flat would be G major. But this is not the case. The major scale with one flat is F major scale. The notes are F, G, A, Bb, C, D, E. Now why Bb? Why not A#?