It is easier to explain things with CGS units..I mean calorie instead of Joule..
specific heat of water is 1 cal/g/K, so ms(deltaT)=1000*1*80=80000 calories required for water to reach zero degree
latent heat of fusion of ice is 80cal/g, so mL=1000*80=80000 calories required for ice to reach water at zero degree
So, the mixture is water at zero degree.