a : b = 2 : 1, b : c = 1 : 3, c : d = 2 : 3, d : e = 1 : 2 Find a : b: c : d : e

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Solution

Given $a : b = 2 : 1$
$b : c = 1 : 3$
$c : d = 2 : 3$
$d : e = 1 : 2$
$\frac{a}{b} = \frac{2}{1} \Rightarrow \frac{a}{2} = b$
also $\frac{b}{c} = \frac{1}{3} \Rightarrow \frac{a / 2}{c} = \frac{1}{3}$
$\Rightarrow \frac{a}{2 c} = \frac{1}{3}$
$\Rightarrow \frac{3 a}{2} = c$
also $\frac{c}{d} = \frac{2}{3} \Rightarrow \frac{3 a / 2}{d} = \frac{2}{3}$
$\Rightarrow \frac{3 a}{2 d} = \frac{2}{3}$
$\Rightarrow \frac{9 a}{4} = d$
also $\frac{d}{e} = \frac{1}{2} \Rightarrow \frac{9 a / 4}{e} = \frac{1}{2}$
$\Rightarrow \frac{9 a}{4 e} = \frac{1}{2}$
$\Rightarrow \frac{9 a}{2} = e$
$∴ a : b : c : d : e = a : \frac{a}{2} : \frac{3 a}{2} : \frac{9 a}{4} : \frac{9 a}{2}$
$= 4 a : 2 a : 6 a : 9 a : 18 a$
$= 4 : 2 : 6 : 9 : 18$ .

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a : b = 2 : 1, b : c = 1 : 3, c : d = 2 : 3, d : e = 1 : 2 Find a : b: c : d : e

Given a:b=2:1b:c=1:3c:d=2:3d:e=1:2ab=21⇒a2=balso bc=13⇒a/2c=13⇒a2c=13⇒3a2=calso cd=23⇒3a/2d=23⇒3a2d=23⇒9a4=dalso de=12⇒9a/4e=12⇒9a4e=12⇒9a2=e∴a:b:c:d:e=a:a2:3a2:9a4:9a2=4a:2a:6a:9a:18a=4:2:6:9:18.