Correct Answer: $32 \frac{1}{7}$

Solution : Given: $\sqrt{\frac{\mathrm{a}}{\mathrm{b}}}=\frac{8}{3}-\sqrt{\frac{\mathrm{b}}{\mathrm{a}}}$
⇒ $\sqrt\frac{a}{b} + \sqrt\frac{b}{a} = \frac{8}{3}$
Squaring both sides, we have,
⇒ $\frac{a}{b}+\frac{b}{a}+2=\frac{64}{9}$
⇒ $\frac{a^2 + b^2}{ab} = \frac{64-18}{9}$
⇒ $a^2 + b^2 = \frac{46ab}{9}$
Now, $a-b=10$
Squaring both sides,
⇒ $a^2 + b^2 - 2ab = 100$
⇒ $\frac{46ab}{9} - 2ab = 100$
⇒ $46ab - 18ab = 900$
⇒ $28ab = 900$
$\therefore ab = \frac{900}{28}=32\frac{1}{7}$
Hence, the correct answer is $32\frac{1}{7}$.