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If A : B=2: 3, B:C=4:5, and C:D=6:7 then A: B: C: D is

A
$$\textbf{16:24:30:35}$$
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Correct option is A. $$\textbf{16:24:30:35}$$

$$A:B=2:3\\ \cfrac{A}{B}=\cfrac{2}{3}\\B:C=4:5\\ \cfrac{B}{C}=\cfrac{4}{5}\\C:D=6:7\\ \cfrac{C}{D}=\cfrac{6}{7}\\ \cfrac{A}{B}=\cfrac{2\times8}{3\times8}=\cfrac{16}{24}\\ \cfrac{B}{C}=\cfrac{4\times6}{5\times6}=\cfrac{24}{30}\\ \cfrac{C}{D}=\cfrac{6\times5}{7\times 5}=\cfrac{30}{35}\\A:B:C:D=16:24:30:35$$

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