Question

3a+5b /3a-5b =5 than a:b

Answer 1

$\frac{3a + 5b}{3a - 5b} = 5$


By componendo and dividendo, we get


$\frac{3a + 5b + 3a - 5b}{3a + 5b - 3a + 5b} = \frac{5 + 1}{5 - 1} \\ \\ \\ => \frac{6a}{10b} = \frac{6}{4} \\ \\ => \frac{a}{b} = \frac{6 \times 10}{4 \times 6} \\ \\ = > \frac{a}{b} = \frac{10}{4} \\ \\ => \frac{a}{b} = \frac{5}{2}$

Answer 2

(3a+5b)/(3a-5b) = 5
3a+5b = 5(3a-5b)
3a+5b = 15a-25b
15a-3a = 5b+25b
12a = 30b
a/b = 30/12

a:b = 30:12
a:b = 10:4
a:b = 5:2