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Question
If a, b, c and d are in proportion, prove that: (ma + nb) : b = (mc + nd) : d
Solution
∵ a, b, c, d are in proportion
`a/b = c/d` = k(say)
a = bk, c = dk.
(ma + nb) : b = (mc + nd) : d
⇒ `"ma + nb"/b = "mc + nd"/d`
L.H.S. = `"mbk + nb"/b`
= `(b("mk + n"))/b`
= mk + n
R.H.S. = `"mc + nd"/d`
= `"mdk + nd"/d`
= `(d("mk + n"))/d`
= mk + n.
∴ L.H.S. = R.H.S.
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