An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity…
An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity of ice melts in 20 minutes, $\mathrm{x}_0$ is the initial quantity of ice. If after 40 minutes the amount of ice left is $\mathrm{Kx}_0$, then $\mathrm{K}=$
$\frac{1}{2}$
$\frac{1}{8}$
$\frac{1}{4}$
$\frac{1}{3}$
Solution
Half the quantity of ice melts in 20 minutes and $\mathrm{x}_0$ is the initial quantity of ice.
$\therefore$ Quantity after 20 minutes $=\frac{\mathrm{x}_0}{2}$
Quantity after 40 minutes $=\frac{1}{2}\left(\frac{x_0}{2}\right)=\frac{x_0}{4}$