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Question
If p + r = 2q and `(1)/q + (1)/s = (2)/r`, then prove that p : q = r : s.
Solution
`(1)/q + (1)/s = (2)/r`
⇒ `(s + q)/(qs) = (2)/r`
⇒ 2qs = r(s + q)
⇒ (p + r)s = r(s + q)
⇒ ps + rs = rs + rq
⇒ ps = rq
⇒ `p/q = r/s`.
Hence proved.
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