MHT CET · Maths · Differential Equations
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 \(\frac{1}{8}\)
- C \(\frac{1}{4}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
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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