A piece of ice has a stone in it and floats in a vessel containing water. When the ice melts, the level of water in the vessel would

Let the mass of ice and stone be $m_{ice}$  and $m_{stone}$  respectively. When both float together in water, then volume of water displaced is

$V_{initial}=\frac{m_{ice}+m_{stone}}{{\rho }_w}$

                        $\left\{\because V_{initial}{\rho }_{w}g=\left(m_{ice}+m_{stone}\right)g\right\}$

Where ${\rho }_w$  is the density of water.

Finally, when the ice melts, then the mass $m_{ice}$  gets converted to water of volume

$V_1=\frac{m_{ice}}{{\rho }_w}$

Further, the stone sinks to the bottom as a result of which a volume $V_2$  of water is displaced by it.

So,

$V_2=\frac{m_{stone}}{{\rho }_{stone}}$

So, total final volume displaced is

$V_{final}=\frac{m_{ice}}{{\rho }_w}+\frac{m_{stone}}{{\rho }_{stone}}$

Since ${\rho }_{stone}>{\rho }_w$ , so

$V_{final}<V_{initial}$

i.e. volume of water displaced when the ice melts and stone sinks is less than the volume displaced. Hence the level of water will fall.