Question

If $\frac{2x-3y}{5x-4y}=\frac{3}{2}$, then the value of $\frac{7x+4y}{7x-4y}$ is

• A. $\frac{42}{19}$
• B. $\frac{43}{17}$
• C. $-43$
• D. $43$

Answer 1

The correct option is C $-43$

$\frac{2x-3y}{5x-4y}=\frac{3}{2}$
$\Rightarrow 2(2x-3y)=3(5x-4y)$
$\Rightarrow \frac{x}{y}=\frac{6}{11}$
$\Rightarrow \frac{7x}{4y}=\frac{42}{44}=\frac{21}{22}$
Applying componendo and dividendo, we get
$\frac{7x+4y}{7x-4y}=\frac{43}{-1}=-43$