Push-ups mainly exercise the strength of the upper body and arms, which is not helpful to lose weight. They are basically shaping and improving strength.

How long you can lose weight depends on your personal situation: diet and intake, exercise intensity, personal physique and so on are all very important factors.

Personally, I think the key to losing weight is diet.

If possible, you should consult relevant professionals and make a reasonable diet training plan in order to lose weight healthily and effectively.