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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 $\mathrm{K}=$
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The correct answer is:
$\frac{1}{4}$
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 $=\frac{1}{2}\left(\frac{x_0}{2}\right)=\frac{x_0}{4}$
$\therefore$ Quantity after 20 minutes $=\frac{\mathrm{x}_0}{2}$
Quantity after 40 minutes $=\frac{1}{2}\left(\frac{x_0}{2}\right)=\frac{x_0}{4}$
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