Question
If $a : b :: c : d$, prove that $\frac{2 a+5 b}{2 a-5 b}=\frac{2 c+5 d}{2 c-5 d}$
✓
Answer
$
\begin{aligned}
& a : b :: c : d \\
& \text { then } \frac{a}{b}=\frac{c}{d} \\
& \Rightarrow \frac{2 a}{5 b}=\frac{2 c}{5 d} \ldots\left(\text { multiply by } \frac{2}{5}\right)
\end{aligned}
$
Applying componendo and dividendo,
$
\frac{2 a+5 b}{2 a-5 b}=\frac{2 c+5 d}{2 c-5 d}
$
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