An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half of the…
An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half of the quantity of ice melts in 15 minutes. $x_0$ is the initial quantity of ice. If after 30 minutes the amount of ice left is $k x_0$, then the value of $k$ is
$\frac{1}{2}$
$\frac{1}{3}$
$\frac{1}{4}$
$\frac{1}{8}$
Solution
Given that half of the ice melts in 15 minutes.
$\therefore \quad$ In 30 minutes, $\left(\frac{1}{4}\right)^{\text {th }}$ of the ice will melt.
$\therefore \quad \mathrm{k}=\frac{1}{4}$