If a : b = 2 : 3, then (5a + 3b) : (6a — 2b) is equal to:

​Given that,

$$a : b = 2 : 3​$$

Let $$\dfrac{a}{b} =\dfrac{2}{3} =k$$

So, $$a=2k $$ and $$b=3k$$

Now substituting the values in the below,

$$\Rightarrow \dfrac{(5a + 3b)}{ (6a — 2b)​}=\dfrac{(5\times 2k + 3\times 3k)}{ (6\times2k — 2\times3k)​}​$$

$$\Rightarrow \dfrac{(5\times 2k + 3\times 3k)}{ (6\times2k — 2\times3k)​}=\dfrac{10k+9k}{12k-6k}​$$​

$$\Rightarrow \dfrac{10k+9k}{12k-6k}​=\dfrac{19k}{6k}$$​​

$$\Rightarrow \dfrac{19}{6}$$

Hence the required ratio 19:6