Question

Q1.If (3a+5b):(3a-5b)=5:1.

Answer 1

Step-by-step explanation:

We can either use cross multiplication or componendo and dividendo.

Method - 1

$\begin{gathered} \frac{3a + 5b}{3a - 5b} = \frac{5}{1} \\ \\ 1(3a + 5b) = 5(3a - 5b) \\ \\ 3a + 5b = 15a - 25b \\ \\ 5b + 25b = 15a - 3a \\ \\ 30b = 12a \\ \\ \frac{ a}{b} = \frac{30}{12} \\ \\ \frac{a}{b} = \frac{5}{2} \end{gathered}$

Therefore, a : b = 5 : 2

Method - 2

$\begin{gathered}\frac{3a + 5b}{3a - 5b} = \frac{5}{1} \\ \\ \frac{(3a + 5b) + (3a - 5b)}{(3a + 5b) - (3a - 5b)} = \frac{5 + 1}{5 - 1} \\ \\ \frac{6a}{10b} = \frac{6}{4} \\ \\ \frac{ a}{b} = \frac{10}{4} \\ \\ \frac{a}{b} = \frac{5}{2} \end{gathered}$

Therefore, a : b = 5 : 2.