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(B) Let $x$ be the assets at time $t$. Given $\frac{dx}{dt} = k \sqrt{x}$.Separating variables,we get $\frac{dx}{\sqrt{x}} = k dt$.Integrating both si

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$42.25$ crores

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(B) Let $x$ be the assets at time $t$. Given $\frac{dx}{dt} = k \sqrt{x}$.Separating variables,we get $\frac{dx}{\sqrt{x}} = k dt$.Integrating both sides,$\int x^{-1/2} dx = \int k dt$,which gives $2 \sqrt{x} = kt + C$.At $t = 0$,$x = 9$,so $2 \sqrt{9} = k(0) + C \Rightarrow C = 6$.Thus,$2 \sqrt{x} = kt + 6$.At $t = 2$,$x = 16$,so $2 \sqrt{16} = k(2) + 6 \Rightarrow 8 = 2k + 6 \Rightarrow 2k = 2 \Rightarrow k = 1$.The equation becomes $2 \sqrt{x} = t + 6$.After $5$ more years,$t = 2 + 5 = 7$.Substituting $t = 7$,$2 \sqrt{x} = 7 + 6 = 13$.$\sqrt{x} = 6.5$.$x = (6.5)^2 = 42.25$ crores.

The assets of a person are increasing at a rate proportional to the square root of the assets at a given time. His assets increase from Rupees $9$ crores to Rupees $16$ crores in $2$ years,then his assets at the end of $5$ more years will be

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