If $$a : b = 3 : \sqrt 5$$, then the value of (2a + b) : (3a — 2b) is:

Given,  $$a : b = 3 : \sqrt 5$$

$$=$$>  $$\frac{a}{b}=\frac{3}{\sqrt{5}}$$

$$=$$>  $$a=\frac{3}{\sqrt{5}}b$$

$$\therefore\ $$(2a + b) : (3a - 2b) = $$\frac{2a+b}{3a-2b}$$

$$=\frac{2\left(\frac{3}{\sqrt{5}}b\right)+b}{3\left(\frac{3}{\sqrt{5}}b\right)-2b}$$

$$=\frac{6b+\sqrt{5}b}{9b-2\sqrt{5}b}$$

$$=\frac{6+\sqrt{5}}{9-2\sqrt{5}}\times\frac{9+2\sqrt{5}}{9+2\sqrt{5}}$$

$$=\frac{\left(6+\sqrt{5}\right)\left(9+2\sqrt{5}\right)}{9^2-\left(2\sqrt{5}\right)^2}$$

$$=\frac{54+12\sqrt{5}+9\sqrt{5}+2\left(5\right)}{81-20}$$

$$=\frac{1}{61}\left(64+21\sqrt{5}\right)$$

Hence, the correct answer is Option B