1 kg of ice at 0°C is mixed with 1.5 kg of water at 45°C [latent heat of fusion = 80 cal /g]. Then:

Heat gained by ice = Heat lost by water 

Maximum heat loss by water =

$1.5\times {10}^3\times 45=67.5 \mathrm{kcal}$

$\mathrm{Heat} \mathrm{required} \mathrm{by} \mathrm{ice} \mathrm{to} \mathrm{melt}=80 \mathrm{kcal}$

so all the ice will not melt hence final temperature will be 0⁰C

$\mathrm{Amount} \mathrm{of} \mathrm{ice} \mathrm{melt}=\frac{67.5\times {10}^3}{80}=843.75 g$

Ice remaining = 1000 - 843.75 = 156.25 g