If (x + 3) : (4x + 1) is the duplicate ratio of 3 : 5, find the value of x.

According to question,

$\Rightarrow \dfrac{x + 3}{4x + 1} = \dfrac{3 \times 3}{5 \times 5} \\[1em] \Rightarrow \dfrac{x + 3}{4x + 1} = \dfrac{9}{25} \\[1em] \Rightarrow 25(x + 3) = 9(4x + 1) \\[1em] \Rightarrow 25x + 75 = 36x + 9 \\[1em] \Rightarrow 36x - 25x = 75 - 9 \\[1em] \Rightarrow 11x = 66 \\[1em] \Rightarrow x = 6.$

Hence, x = 6.