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

1. 1 : 2

2. 1 : 4

3. 2 : 1

4. 4 : 1

Given,

$\therefore \dfrac{5a + 3b}{2a - 3b} = \dfrac{23}{5}$

Cross multiplying:

$\Rightarrow 5(5a + 3b) = 23(2a - 3b) \\[1em] \Rightarrow 25a + 15b = 46a - 69b \\[1em] \Rightarrow 25a - 46a = -69b - 15b \\[1em] \Rightarrow -21a = -84b \\[1em] \Rightarrow 21a = 84b \\[1em] \Rightarrow \dfrac{a}{b} = \dfrac{84}{21} = 4.$

Thus,

a : b = 4 : 1.

Hence, option 4 is the correct option.