Ratio and Proportion — Mathematics STD 10 — Question
ICSE BoardEnglish MediumSTD 10MathematicsRatio and Proportion2 Marks
Question
If (ma + nb): b :: (mc + nd) : d, prove that a, b, c, d are in proportion.
✓
Answer
$ \begin{aligned} & ( ma + nb ): b ::( mc + nd ): d \\ & \Rightarrow \frac{ ma + nb }{ b }=\frac{ mc + nd }{ d } \\ & \Rightarrow mad + nbd = mbc + nbd \\ & \Rightarrow mad = mbc \\ & \Rightarrow ad = bc \\ & \Rightarrow \frac{a}{b}=\frac{c}{d} \end{aligned} $ Hence a : b :: c : d.
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