Question

If $\frac{8a-5b}{8c-5d}=\frac{8a+5b}{8c+5d}$, then $\frac{a}{b}=\frac{c}{d}$

• A. True
• B. False

Answer 1

The correct option is A

True

Given, $\frac{8a-5b}{8c-5d}=\frac{8a+5b}{8c+5d}$

$\Rightarrow \frac{8a-5b}{8a+5b}=\frac{8c-5d}{8c+5d}$ [Applying alternendo]

$\frac{8a-5b+8a+5b}{8a-5b-8a-5b}=\frac{8c-5d+8c+5d}{8c-5d-8c-5d}$ [Applying componendo and dividendo]

$\frac{16a}{-10b}=\frac{16c}{-10d}$

$\frac{a}{b}=\frac{c}{d}$

Hence, the above statement is true.