If 5a + 3b : 2a - 3b = 23 : 5, then the value of a : b is

Answer: Option D

$$\begin{array}{rl}& =\frac{5a+3b}{2a-3b}=\frac{23}{5}\\ & \Rightarrow 5\left(5a+3b\right)=23(2a-3b)\\ & \Rightarrow 25a+15b=46a-69b\\ & \Rightarrow 21a=84b\\ & \Rightarrow \frac{a}{b}=4.\\ & \text{Hence},a:b=4:1\end{array}$$