Let rate of upstream = x kmph and rate of downstream = y kmph.

Then, $\frac{24}{\mathrm{x}}+\frac{36}{\mathrm{y}}=6\dots .\left(\mathrm{i}\right)$ and $\frac{36}{\mathrm{x}}+\frac{24}{\mathrm{y}}=\frac{13}{2}\dots .\left(\mathrm{i}\mathrm{i}\right)$

Solving (i) & (ii) $\mathrm{y}=12\mathrm{ }\mathrm{km} {\mathrm{hr}}^{-1}$ and $x=8 \mathrm{km} {\mathrm{hr}}^{-1}$

$\therefore$Speed upstream = 8 kmph, Speed downstream = 12 kmph.

Hence, rate of current $=\frac{1}{2}\left(12-8\right)$ kmph = $2 \mathrm{kmph}$.
and rate of Boat $=\frac{1}{2}\left(12+8\right)=10\mathrm{ }\mathrm{kmph}$