If a : b = 3 : 5, find (3a + 5b) : (7a - 2b).

Given,

$\dfrac{a}{b} = \dfrac{3}{5} \\[1em] \therefore a = \dfrac{3b}{5}$

Putting value of a in the ratio (3a + 5b) : (7a - 2b),

$= \dfrac{3 \times \dfrac{3b}{5} + 5b}{7 \times \dfrac{3b}{5} - 2b} \\[1em] = \dfrac{\dfrac{9b}{5} + 5b}{\dfrac{21b}{5} - 2b} \\[1em] = \dfrac{\dfrac{9b + 25b}{5}}{\dfrac{21b - 10b}{5}} \\[1em] = \dfrac{34b}{11b} \\[1em] = \dfrac{34}{11} = 34 : 11.$

Hence, the value of ratio (3a + 5b) : (7a - 2b) is 34 : 11.