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Mathematics

If p : q = r : s; then show that:

mp + nq : q = mr + ns : s

Ratio Proportion

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Answer

Given,

⇒pq=rs\Rightarrow \dfrac{p}{q} = \dfrac{r}{s}

Multiplying both sides by m:

⇒mpq=mrs\Rightarrow \dfrac{mp}{q} = \dfrac{mr}{s}

Adding n on both sides:

⇒mpq+n=mrs+n⇒mp+nqq=mr+nss\Rightarrow \dfrac{mp}{q} + n = \dfrac{mr}{s} + n \\[1em] \Rightarrow \dfrac{mp + nq}{q}= \dfrac{mr + ns}{s}

Hence, proved that mp + nq : q = mr + ns : s.

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