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Question
If ( a+c) : b = 5 : 1 and (bc + cd) : bd = 5 : 1, then prove that a : b = c : d
Solution
`("a + c")/"b" = 5/1`
⇒ a + c = 5b
`("bc + cd")/"bd" = 5/1`
⇒ bc + cd = 5bd
⇒ bc +cd = (a + c)d
⇒ bc + cd = ad + cd
⇒ bc = ad
⇒ `"a"/"b" = "c"/"d"`
Hence a : b = c : d
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