MHT CET · Maths · Differential Equations
The assets of a person reduced in his business such that the rate of reduction is proportional to the square root of the existing assets. If the assets were initially ₹ 10 lakhs and due to loss they reduce to ₹ \(10000\) after 3 years, then the number of years required for the person to be bankrupt will be
- A \(\frac{20}{3}\) years
- B \(\frac{10}{3}\) years
- C \(\frac{10}{9}\) years
- D \(\frac{20}{9}\) years
Answer & Solution
Correct Answer
(B) \(\frac{10}{3}\) years
Step-by-step Solution
Detailed explanation
\( \frac{dA}{dt} = -k\sqrt{A} \) \( \int \frac{dA}{\sqrt{A}} = \int -k dt \Rightarrow 2\sqrt{A} = -kt + C \)
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