If (a - b) : (a + b) = 1 : 11, find the ratio (5a + 4b + 15) : (5a - 4b + 3).

Given,

$\phantom{\Rightarrow} \dfrac{a - b}{a + b} = \dfrac{1}{11} \\[1em] \Rightarrow 11(a - b) = a + b \\[1em] \Rightarrow 11a - 11b = a + b \\[1em] \Rightarrow 11a - a = b + 11b \\[1em] \Rightarrow 10a = 12b \\[1em] \Rightarrow a = \dfrac{12b}{10} \\[1em] \Rightarrow a = \dfrac{6b}{5}.$

Substituting value of a in (5a + 4b + 15) : (5a - 4b + 3) we get,

$\Rightarrow \dfrac{5 \times \dfrac{6b}{5} + 4b + 15}{5 \times \dfrac{6b}{5} - 4b + 3} \\[1em] \Rightarrow \dfrac{6b + 4b + 15}{6b - 4b + 3} \\[1em] \Rightarrow \dfrac{10b + 15}{2b + 3} \\[1em] \Rightarrow \dfrac{5(2b + 3)}{2b + 3} \\[1em] \Rightarrow \dfrac{5}{1}.$

Hence, (5a + 4b + 15) : (5a - 4b + 3) = 5 : 1.