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Ratio and Proportion — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsRatio and Proportion1 Mark
Question
If a : b = c : d, prove that: 5a + 7b : 5a – 7b = 5c + 7d : 5c – 7d.
✓

Answer

Given $\frac{a}{b}=\frac{c}{d}$
$\Rightarrow \frac{5 a}{7 b}=\frac{5 c}{7 d}$ (Multiplying each side by 5/7)
$\Rightarrow \frac{5 a+7 b}{5 a-7 b}=\frac{5 c+7 d}{5 c-7 d}$ (By componendo and dividendo)

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