As we know there are two main common meter :- simple and compound. We all know that simple meter divides a beat into two and compound meter into three. We also know that a measure holding two beat is duple, three beat triple and four beat quadruple so on. Now my question rise here. I saw some where in internet a music sheet using 2/4 meter which seems "simple duple". 2 beat in each measure "duple" and it would have been normal if a quarter note or eighth note use those beat space because they can be divided into two which make sense to be a simple. But a triplet? I found they using two triplet of eight note which we know 1-triplet = 1 beat so, 2-triplet = 2 beat. It fitted fine with the 2/4 time signature in the view of "duple" I think we can say two dotted quarter note made a triplet (if i'm wrong at this point tell me guys). But in view of "simple" a triplet seems to be divided in three part of a note then how is it fitted on "simple" ? If triplet is a note divided in three then isn't it suitable to be in compound? Is 2/4 meter really a compound duple or simple duple? Please help me to clear my misunderstanding.
If ALL the notes relate to triplets, then you will have six quaver triplets per bar, and it would be better written in 6/8 (compound duple). If only some bars have triplets, and others contain the normal 4 quavers, 2 crotchets, or a combination, the time sig will probably stay as simple duple, 2/4. So, it depends on the writer and the tune itself. One will always be a better fit than the other.
2/4 is a simple duple meter. It doesn't matter how many triplets, quintuplets, septuplets, or any other tuplets are in the music--it's still a simple duple meter.
Now, if you notate all eighth-note triplets and no other tuplets (including bog-standard duplets) in the entire 2/4 piece, people may argue that your music should be in 6/8 (a compound duple meter) instead.
(I'm answering based on my best understanding of your question. I hope I'm interpreting your words right...)
I think you have a very cursory understanding of what a Time Signature is. The beats of time signatures can have any number of notes in them. Compound vs Simple is much more an issue of what beats consist of.
Compound time has dotted note values for beats where Simple time simply has notes without dots for beats, this has very little to do with what particular notes a beat can or should consist of.
A compound time signature can have two notes in a bar trough the use of duplets, just in the same way as a simple time signature can have three notes in a beat trough the use of triplets