If $$a=\frac{3}{7}b$$​, then the value of $$\frac{(8a-b)}{(2a+3b)}$$​ is:

Correct option is D

Given:

​$$a = \frac{3}{7} b \\$$​​

Solution:

​$$\frac{a}{b} = \frac{3}{7} \\a : b = 3 : 7 \\\text{let } a = 3x \text{ and } b = 7x \\\frac{8a - b}{2a + 3b} \\= \frac{[ (8 \times 3x) - 7x ]}{[ (2 \times 3x) + (3 \times 7x) ]} \\= \frac{(24x - 7x)}{(6x + 21x)} \\= \frac{17x}{27x} \\= \frac{17}{27} \\$$​​

The value of $$\frac{8a - b}{2a + 3b} \text{ is } \frac{17}{27}.$$​​