Find the value of x, if (2x + 1) : (3x + 13) is the sub-duplicate ratio of 9 : 25

According to question,

$\Rightarrow \dfrac{2x + 1}{3x + 13} = \dfrac{\sqrt{9}}{\sqrt{25}} \\[1em] \Rightarrow \dfrac{2x + 1}{3x + 13} = \dfrac{3}{5} \\[1em] \Rightarrow 5(2x + 1) = 3(3x + 13) \\[1em] \Rightarrow 10x + 5 = 9x + 39 \\[1em] \Rightarrow 10x - 9x = 39 - 5 \\[1em] \Rightarrow x = 34.$

Hence, x = 34.