If a : b = c : d, then (ma+nc) / mb+nd is equal to : 1. m : n 2. dm : cn 3. an : mb 4. a : b

Mathematics

If a : b = c : d, then $\dfrac{ma + nc}{mb + nd}$ is equal to :
m : n
dm : cn
an : mb
a : b

Ratio Proportion

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Answer

Given,

⇒ a : b = c : d

$\Rightarrow \dfrac{a}{b} = \dfrac{c}{d}$

Let, $\dfrac{a}{b} = \dfrac{c}{d}$ = k where k is the constant ratio.

Therefore, a = bk and c = dk

Substituting values of a and c in $\dfrac{ma + nc}{mb + nd}$ , we get :

$\Rightarrow \dfrac{m(bk) + n(dk)}{mb + nd} \\[1em] \Rightarrow \dfrac{k(mb + nd)}{mb + nd} \\[1em] \Rightarrow k \\[1em] \Rightarrow \dfrac{a}{b} \\[1em] \Rightarrow a : b.$

Hence, option 4 is the correct option.

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Mathematics

If a : b = c : d, then $\dfrac{ma + nc}{mb + nd}$ is equal to :
m : n
dm : cn
an : mb
a : b

Ratio Proportion

Answer

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Mathematics

If a : b = c : d, then ma+ncmb+nd\dfrac{ma + nc}{mb + nd}mb+ndma+nc​ is equal to :m : ndm : cnan : mba : b

Ratio Proportion

Answer

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