Q54 / 150 · MHT CET 2021 (20 Sep Shift 1) · Mathematics

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 $\mathrm{K}=$

  • A
    $\frac{1}{2}$
  • B
    $\frac{1}{8}$
  • Correct answer
    C
    $\frac{1}{4}$
  • D
    $\frac{1}{3}$

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 $=\frac{1}{2}\left(\frac{x_0}{2}\right)=\frac{x_0}{4}$

Hence, the correct answer is option: 'C'.

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