If $latex a:b=\frac{2}{9}:\frac{1}{3}, b:c=\frac{2}{7}:\frac{5}{14} $ and $latex d:c=\frac{7}{10}:\frac{3}{15} $, then find a:b:c:d

If $latex a:b=\frac{2}{9}:\frac{1}{3}, b:c=\frac{2}{7}:\frac{5}{14} $ and $latex d:c=\frac{7}{10}:\frac{3}{15} $, then find a:b:c:d
[A]56:84:30:30
[B]16:24:30:35
[C]56:24:30:30
[D]56:24:30:35

16:24:30:35
$latex \because a:b=2:3, b:c=4:5 $ and $latex c:d=6:7 $
=>$latex a:b=2:3, b:c=1:\frac{5}{4} $ and $latex c:d=1:\frac{7}{6} $
=>$latex a:b=2:3, b:c=3:\frac{15}{4} $ and $latex c:d=\frac{15}{4}:\frac{7}{6}\times \frac{15}{4} $
=>$latex a:b=2:3, b:c=3:\frac{15}{4} $ and $latex c:d=\frac{15}{4}:\frac{35}{8} $
=>$latex a:b:c:d:=2:3:\frac{15}{4}:\frac{35}{8}=16:24:30:35 $
Hence option [B] is the tight answer.


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