Infographic: Ratio & Proportion | Quantitative Aptitude (Quant) - CAT PDF Download

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Infographic: Ratio and Proportion
What is Ratio?
Comparison of two similar quantities using division: a : b 
or a/b. Has no units. In a : b, 'a' is antecedent, 'b' is 
consequent.
What is Proportion?
Equality of two ratios: a : b = c : d. Here a and d are 
extremes, b and c are means. Product of means = 
Product of extremes.
Key Properties of Ratio
Multiplication/Division 
Rule
Ratio remains same if both terms 
multiplied or divided by same 
non-zero number. Example: 5:9 = 
10:18 = 15:27
Comparison
Two ratios in fraction form can 
be compared like real numbers. 
Units must be similar for valid 
comparison.
Order Matters
Significant order of terms must 
be maintained. Quantities must 
be of same kind.
Types of Ratios
Compounded Ratio
Ratios (a:b), (c:d), (e:f) = (ace:bdf)
Duplicate & Sub-duplicate
Duplicate: (a²:b²)
Sub-duplicate: (:a::b)
Triplicate & Sub-triplicate
Triplicate: (a³:b³)
Sub-triplicate: (a^(1/3):b^(1/3))
Componendo & Dividendo
Special rule for ratio manipulation
Important Properties of Proportion
1 Product Rule
If a:b = c:d, then ad = bc (Product of extremes = 
Product of means)
2 Continued Proportion
a:b = b:c = c:d
3
Mean Proportional
If a:b = b:c, then b² = a × c
4
Third & Fourth Proportional
If a:b = b:c, c is third proportional. If a:b = c:d, d is 
fourth proportional.
Variations
1
Direct Proportion
a = kb (constant k). Written as: a ? b
2
Indirect Proportion
ab = k (constant k). Written as: a ? 1/b
Quick Method for Chain Ratios
Shortcut Technique: For A:B = 1:2, B:C = 2:3, C:D = 5:6, D:E = 7:8
Combined ratio A:B:C:D:E = (1×2×5×7):(2×2×5×7):(2×3×5×7):(2×3×6×7):(2×3×6×8) = 70:140:210:252:288
Each term takes products of denominators before it and numerators after it.
Key Differences
Ratio
Compares two quantities
Written as a:b or a/b
No units, abstract quantity
Shows relative size
Proportion
Equality of two ratios
Written as a:b = c:d or a:b::c:d
Shows equivalence
Product of extremes = Product of means