Question

if a:b=c:d=e:f all ratio =5a-7c-13e/5b-7d-13f​

Answer 1

$Let \: \frac{a}{b} = \frac{c}{d} = \frac{e}{f} = k$

$\blue { k \: is \: any \:real \: number }$

$\frac{a}{b} = k \implies a = bk \: ---(1)$

$\frac{c}{d} = k \implies c = dk \: ---(2)$

$\frac{e}{f} = k \implies e = fk \: ---(3)$

$Now, ratio = \frac{5a-7c-13e}{5b-7d-13f} \\= \frac{5bk -7dk -13fk}{5b-7d-13f}\\ [ From \: (1),\: (2) \:and \:(3) ]$

$= \frac{k(5b -7d -13f}{5b-7d-13f}\\= k$

Therefore.,

$\red {ratio = \frac{5a-7c-13e}{5b-7d-13f}}\green {= k : 1 }$

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