Will i lose 1 kg a week if i eat less than 1200 calories a day and burn 400 through exercise? (thats 800 calories i am consuming a day)?

That's very little calories per day (body needs 2,000 for daily function), it's very unhealthy, why not eat the regular 2000, and do a lot of cardio? Running etc... is your best bet. Remember losing weight is a long term process so don't sweat it.

Really bad for you, your body won't be fooled by eating less your body enters starvation mode, and you lose weight much slower and when you get gain back the weight much faster

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