Question
If $a : e = 5 : 12, e : i = 8 : 3$ and $i : u = 9 : 16,$ then find $a : u$
✓
Answer
$a : e =5: 12 \Rightarrow \frac{ a }{ e }=\frac{5}{12} $
$ e : i =8: 3 \Rightarrow \frac{ e }{ i }=\frac{8}{3} $
$ i : u =9: 16 \Rightarrow \frac{ i }{ u }=\frac{9}{16}$
$\Rightarrow \frac{ a }{ e } \times \frac{ e }{ i } \times \frac{ i }{ u }=\frac{5}{12} \times \frac{8}{3} \times \frac{9}{16} $
$ \Rightarrow \frac{ a }{ u }=\frac{10}{6}=\frac{5}{8} $
$ a : u =5: 8$
$ e : i =8: 3 \Rightarrow \frac{ e }{ i }=\frac{8}{3} $
$ i : u =9: 16 \Rightarrow \frac{ i }{ u }=\frac{9}{16}$
$\Rightarrow \frac{ a }{ e } \times \frac{ e }{ i } \times \frac{ i }{ u }=\frac{5}{12} \times \frac{8}{3} \times \frac{9}{16} $
$ \Rightarrow \frac{ a }{ u }=\frac{10}{6}=\frac{5}{8} $
$ a : u =5: 8$
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