7A. Quick Reference Formula Sheet

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Keep this box handy for last-minute revision before the exam — every formula used in this chapter, in one place:

Concept	Formula
Simplest form of a ratio	Divide both terms by their HCF
Compound ratio of a:b and c:d	(a×c) : (b×d)
Duplicate ratio of a:b	a² : b²
Sub-duplicate ratio of a:b	√a : √b
Triplicate ratio of a:b	a³ : b³
Sub-triplicate ratio of a:b	a^(1/3) : b^(1/3)
Inverse ratio of a:b	b : a
Dividing S in ratio m:n	S×m/(m+n), S×n/(m+n)
Proportion rule	a:b::c:d ⇒ ad = bc
Mean proportional between a, c	√(ac)
Third proportional to a, b	b²/a
Fourth proportional to a, b, c	bc/a
Componendo-Dividendo	if a/b=c/d then (a+b)/(a−b) = (c+d)/(c−d)
Reverse Componendo-Dividendo	if (a+b)/(a−b)=p/q then a/b = (p+q)/(p−q)
Direct proportion	x₁/y₁ = x₂/y₂
Inverse proportion	x₁y₁ = x₂y₂
Simple partnership share	Profit × (own investment)/(total investment)
Compound partnership share	Profit × (own capital×time)/(total capital×time)
“x% more than” as ratio	(100+x) : 100
“x% less than” as ratio	(100−x) : 100

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