Is 4 months a realistic goal to lose weight?

I would like to lose some weight, but not too much. I'm at a healthy weight but at the higher end of the scale, I'm planning to lose some weight (still in the healthy range) to have a more attractive body shape. I know that trying to lose weight fast is not the key (from past experiences) so I would like to know if 4 months is a reasonable and realistic amount of time. I'm going to be dieting but it will mostly just cutting out processed foods and reducing salt and eating more vegetables. I am not planning to count calories either as I've tried and it just doesn't work. Since I have started wanting to lose some weight about 2 years ago I have noticed that I have gained weight but I am still the same height. I am planning of doing daily exercises > 20 minutes treadmill and 30 minutes of sit-ups, push ups, crunches, squats, stretching etc.. per day.

I have tried over a couple years but I seem to always give up and binge eat or give up exercising. This time I am dead serious, I am planning to work hard to become healthier on the inside and out. My plan is I would like to reach my goal by the start of summer in about 20 weeks. If I diet properly and exercise daily would that be a realistic and responsible goal?

I am a 15-year-old Female at 155cm and 52kg (5 foot and 115 pounds)

Any tips?

Any information would be helpful, if you have any question you want answered then mention it and I'll check your question out as well.