A piece of ice, with a stone frozen inside it, is floating in water contained in a beaker. When the ice melts, the level of water in the beaker                      

Given that

A piece of ice with stone frozen inside it is floating in water.

That means (mass of ice + mass of stone) g = (mass of water displaced) g

When ice melts into water.

The stone is separated and it can not displace individually water equal to its weight and its sinks into water.

So weight of water displaced by molten ice + weight of water displaced by separated stone < weight of water ice and stone together displaced before melting.

Hence the level of water falls.