The assets of a person reduced in his business such that the rate of reduction is proportional to the square…

If $A$ denotes the assets at time $t$, the rate of reduction is proportional to $\sqrt{A}$, so

$\frac{dA}{dt} = -k\sqrt{A}$

Separating and integrating gives

$\int A^{-1/2}\,dA = \int -k\,dt$

$2\sqrt{A} = -kt + C$

At $t = 0$, $A = 10^6$, hence $2\sqrt{10^6} = C$, so $C = 2000$.

At $t = 3$, $A = 10^4$, giving $2\sqrt{10^4} = -3k + 2000$
$200 = -3k + 2000$
$k = 600$

The solution becomes $2\sqrt{A} = -600t + 2000$.
Set $A = 0$ for bankruptcy: $0 = -600t + 2000$, so $t = \frac{2000}{600} = \frac{10}{3}$ years.

Correct choice is B.