If the ratio of 8 and 11 is same as the ratio of 2x - y to x + 2y, find the value of $\dfrac{7x}{9y}$.

According to question,

$\phantom{\Rightarrow} \dfrac{2x - y}{x + 2y} = \dfrac{8}{11} \\[1em] \Rightarrow 11(2x - y) = 8(x + 2y) \\[1em] \Rightarrow 22x - 11y = 8x + 16y \\[1em] 22x - 8x = 16y + 11y \\[1em] 14x = 27y \\[1em] x = \dfrac{27y}{14}.$

Substituting value of x in $\dfrac{7x}{9y}$ we get,

$\dfrac{7x}{9y} = \dfrac{7}{9y} \times \dfrac{27y}{14} \\[1em] = \dfrac{3}{2}.$

Hence, $\dfrac{7x}{9y} = \dfrac{3}{2}$.