Percentage & Ratio Formula
Percentage & Ratio formulas and a topic-wise mock test for quantitative aptitude placement exams like TCS NQT, Infosys, and Wipro. Revise, then practice.
Key Percentage & Ratio Formulas
Percentage Fundamentals - The Building Blocks
Percentage is a way to express a number as a fraction of 100. It's one of the most commonly used mathematical concepts in daily life, business, and competitive exams.
- Basic Formula: Percentage = (Part/Whole) × 100
- Finding Part: Part = (Percentage × Whole) / 100
- Finding Whole: Whole = (Part × 100) / Percentage
- Percentage Change: ((New Value - Old Value) / Old Value) × 100
- Successive Percentage: Final = Original × (1 ± p1/100) × (1 ± p2/100)
- Example: Price increases 10% then decreases 5% → Final = Original × 1.10 × 0.95
Ratio & Proportion - Comparative Mathematics
Ratio compares two quantities by division, while proportion states that two ratios are equal. These concepts are fundamental in solving problems involving comparisons, mixtures, time and work.
- Ratio Definition: a:b = a/b (simplified form)
- Proportion: a:b :: c:d means a/b = c/d
- Mean Proportion: If a:b :: b:c, then b² = ac
- Third Proportion: If a:b :: b:c, then c = b²/a
- Fourth Proportion: If a:b :: c:d, then d = bc/a
- Compound Ratio: (a:b) × (c:d) = ac:bd
Mixture & Alligation - Advanced Percentage Applications
Mixture and alligation problems involve combining different ingredients with different characteristics to achieve a desired result.
- Alligation Rule: (Cheaper - Mean) / (Mean - Dearer) = Quantity of Dearer / Quantity of Cheaper
- Weighted Average: (n1×a1 + n2×a2) / (n1 + n2)
- Replacement Formula: Final = Initial × (1 - r/100)^n
- Example: Mix 60% and 80% solutions to get 70% → Ratio = (80-70):(70-60) = 1:1
Back to Quantitative Aptitude practice