Question

If $\frac{a}{b}=\frac{6}{7}$, then value of $\frac{2a+7b}{2a-7b}$ is

• A. $-\frac{14}{13}$
• B. $-\frac{59}{37}$
• C. $-\frac{61}{37}$
• D. $-\frac{73}{37}$

Answer 1

The correct option is C $-\frac{61}{37}$

$\frac{a}{b}=\frac{6}{7}$
$\Rightarrow \frac{2a}{7b}=\frac{12}{49}$
Applying componendo and dividendo, we get
$\frac{2a+7b}{2a-7b}=\frac{12+49}{12-49}=-\frac{61}{37}$