Question

If



a.b = 5:7 , b:c = 8:9, c:d = 3:5 then find the ratio of a:d 3:10 4:9 5:13 8:21

Answer 1

Hope u like my process
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$= > \it \: ratios \: \: of \: \: a : b = 5 : 7 \\ \\ = > ratios \: \: of \: \: b : c = 8 : 9 \\ \\ = > ratios \: \: of \: \: c : d = 3 : 5$
To get the required form in a single ratio is can be done as

$= >a : c \\ \\ = > \bf \: a : b : : b : c \\ \\ = > \it \: \frac{a}{b} : \frac{c}{b} \\ \\ = > \frac{5}{7} : \frac{9}{8} \\ \\ = > \frac{5 \times 8}{7 \times 9} = \frac{40}{63} \\ \\ = > \bf 40 : 63$

Similarly...

$= > \bf \: a : d \\ \\ = > \it a : c : : c : d \\ \\ = > \frac{a}{c} : \frac{d}{c} \\ \\ = > \frac{40}{63} : \frac{5}{3} \\ \\ = > \frac{40}{63} \times \frac{3}{5} = \frac{8}{21} \\ \\ = > \bf \: \underline{ \: 8 : 21 \: }$

So the required ratio of a:d = 8:21
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