If (5x - 2y): (x - 2y) = 9: 17, then find the value of $$\frac{9x}{13y}.$$​

Correct option is C

Given:
(5x - 2y) ∶ (x - 2y) = 9 ∶ 17
Solution:
​$$\frac{5x - 2y}{x - 2y} = \frac{9}{17} \\17 \times (5x - 2y) = 9 \times (x - 2y) \\85x - 34y = 9x - 18y \\76x = 16y \\\frac{x}{y} = \frac{16}{76} \\\frac{x}{y} = \frac{4}{19} \\\frac{9 \times \frac{4}{19}}{13} = \frac{36}{247} \\\therefore \frac{9x}{13y} = \frac{36}{247}.$$​​