If $(3 a + 2 b) : (5 a + 3 b) = 18 : 29$ . Find $a : b$

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Solution

Given: $(3 a + 2 b) : (5 a + 3 b) = 13 : 29$
$\Rightarrow \frac{3 a + 2 b}{5 a + 3 b} = \frac{18}{29}$
$\Rightarrow 87 a + 58 b = 90 a + 54 b$
$\Rightarrow 3 a = 4 b$
$\frac{a}{b} = \frac{4}{3}$

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