Ratio and Proportion: Techniques

Basic Concepts

• Ratio a:b means a/b
• If a:b = c:d, then ad = bc (cross multiplication)
• Componendo-Dividendo: If a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d)

Combining Ratios

• If A:B = 2:3 and B:C = 4:5
• Make B equal: A:B:C = 8:12:15

Direct and Inverse Proportion

• Direct: If x increases, y increases (x/y = constant)
• Inverse: If x increases, y decreases (xy = constant)

Partnership

• Simple: Profit ratio = Investment ratio
• Compound: Profit ratio = (Investment × Time) ratio

Mixture and Alligation

• Mean price = (Quantity₁ × Price₁ + Quantity₂ × Price₂) / (Quantity₁ + Quantity₂)
• Alligation rule: (Cheaper quantity)/(Dearer quantity) = (Dearer price - Mean)/(Mean - Cheaper price)

CAT Tip

Use LCM method to combine ratios quickly - saves 30-40 seconds.