120g of ice at $0°C$ is mixed with 100g of water at $80°C$ . Latent heat of fusion of water is $80cal{g}^{-1}$ and specific heat of water is $1cal{g}^{-1}°C^{-1}$. The final temperature of the mixture is 

Heat rejected by 100g of water at  $80°C$ when its temperature becomes $0°C$ is 
 $Q=ms\Delta \theta =\left(100\right)\left(1\right)\left(80\right)=8000cal$
But this heat can melt $m=\frac{Q}{L}=\frac{8000}{80}=100g$ of ice only.
Hence, the temperature of the mixture is$0°C$.