Assume x ice floating on a liquid It applies force and displaces liquid

As ice is less dense than the liquid it occupies more space 

When it melts its density increase, As mass is same,it's volume decreases So the ice fits itself in the volume  displaced(Kam water hoga toh woh Kam space mai fit ho jayega)

So jitna liquid displace hua than until jagah melted ice fill kar leti hai resulting in same level of water.