If a : b = 3 : 11, find (15a - 3b) : (9a + 5b).

a : b = 3 : 11 or,

$\dfrac{a}{b} = \dfrac{3}{11}$

We need to find $\dfrac{15a - 3b}{9a + 5b}$

Dividing the numerator and denominator by b,

$\Rightarrow \dfrac{\dfrac{15a}{b} - \dfrac{3b}{b}}{\dfrac{9a}{b} + \dfrac{5b}{b}} \\[0.5em] \Rightarrow \dfrac{\dfrac{15a}{ b} - 3}{\dfrac{9a}{b} + 5} \\[0.5em]$

Putting value of $\dfrac{a}{b} = \dfrac{3}{11}$,

$\Rightarrow \dfrac{15 \times \dfrac{3}{11} - 3}{9 \times \dfrac{3}{11} + 5} \\[0.5em] \Rightarrow \dfrac{\dfrac{45 - 33}{11}}{\dfrac{27 + 55}{11} } \\[0.5em] \Rightarrow \dfrac{12}{82} = \dfrac{6}{41} = 6 : 41$

Hence, the value of ratio is 6 : 41.