Percentage
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Quantitative Aptitude - Percentage
Calculate percentages, increase/decrease, and solve related problems accurately.
1. Basic Definition
Percentage of a number = (part/whole) × 100. Eg: 20% of 250 = (20/100) × 250 = 50.
2. Increase & Decrease
- New value after x% increase = original × (1 + x/100).
- After y% decrease = original × (1 − y/100).
- Sequential changes: multiply factors. Eg: 10% increase then 20% decrease = ×1.1 ×0.8 = ×0.88.
3. Profit, Loss & Discount Link
Profit per cent = (profit/cost) × 100, Loss% = (loss/cost) × 100. Discount% = (discount/marked price) × 100.
4. Quick Tips
- Convert % to fraction or decimal early. Eg: 12.5% = 1/8 = 0.125.
- Use complement for quick mental: Eg: price reduced by 30% → 70% remains.
- For multiple % changes, use sequential multiplication factor.
5. Common Errors
- Misplacing 100 in denominator.
- Ignoring order of operations in sequential changes.
6. Revision Checklist
- Know fraction ↔ percentage conversions.
- Be fluent with increase/decrease formulas.
- Practice sequential % change problems.
Summary: Convert percentages into multipliers early, apply systematically, and verify with simple checks like reverse calculation.
Topics
- Number System
- H.C.F. & L.C.M.
- Decimal Fractions
- Simplification
- Square Roots & Cube Roots
- Average
- Problems on Ages
- Percentage
- Operations on Numbers
- Profit & Loss
- Ratio & Proportion
- Time & Work
- Time & Distance
- Problems on Trains
- Simple Interest
- Compound Interest
- Area
- Volume & Surface Areas
- Mensuration
- Algebra
- Work & Wages
- Geometry (Lines, Angles, Triangles, Polygons)
- Data Interpretation
- Arithmetic Operations