A:B=2:3,B:C=4:5,C:D=6:7 , then A:B:C:D=?

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Solution

Consider the problem

$A : B = 2 : 3$

And,

$\begin{matrix} B : C = 4 : 5 = (4 \times \frac{3}{4} : 5 \times \frac{3}{4}) = 3 : \frac{15}{4} \end{matrix}$

And,

$\begin{matrix} C : D = 6 : 7 = (6 \times \frac{15}{24} : 7 \times \frac{15}{24}) = \frac{15}{4} : \frac{35}{8} \end{matrix}$

So,
$\begin{matrix} A : B : C : D = 2 : 3 : \frac{15}{4} : \frac{35}{8} = 16 : 24 : 30 : 35 \end{matrix}$

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A:B=2:3,B:C=4:5,C:D=6:7 , then A:B:C:D=?

Consider the problemA:B=2:3And,B:C=4:5=(4×34:5×34)=3:154And,C:D=6:7=(6×1524:7×1524)=154:358So,A:B:C:D=2:3:154:358=16:24:30:35