Same chapter4 marksDifficulty: Hard
If a, b and c are in continued proportion, prove that b2 = ac, and hence find b when a = 8 and c = 18 with b positive.
Ratio and Proportion
4 marksDifficulty: Hard
If a/b = c/d, prove that (a + b)/(a − b) = (c + d)/(c − d).
Original Khojo Papers practice question — not from a past board paper.
Answer
The result follows by componendo and dividendo.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
Let a/b = c/d = k, so a = bk and c = dk. Then (a + b)/(a − b) = (bk + b)/(bk − b) = (k + 1)/(k − 1), and (c + d)/(c − d) = (dk + d)/(dk − d) = (k + 1)/(k − 1). The two are equal.
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