Study Notes: Percentage

Overview

Percentage is one of the most fundamental and high-yield topics in SSC CHSL Tier 1 quantitative aptitude. Nearly every arithmetic sub-topic—profit and loss, simple and compound interest, ratio and proportion—builds upon percentage concepts. In the exam, you can expect 2–4 direct questions on percentage, plus another 5–8 questions where percentage is embedded in other topics.

Mastery of percentage means two things: (1) lightning-fast conversion between fractions, decimals and percentages, and (2) the ability to apply percentage increase/decrease formulas to real-world situations like price changes, population growth, salary hikes and exam score analysis. Students who can mentally compute common percentage values (like 12.5% = 1/8 or 16⅔% = 1/6) gain a significant speed advantage.

The topic is entirely formula-driven with minimal theory. Focus on recognizing problem patterns—successive percentage changes, percentage point differences, and reverse percentage calculations are the three most commonly tested variations beyond basic conversion.

Key Concepts

• **Percentage means "per hundred"**: 45% = 45/100 = 0.45. It is a way of expressing a fraction with denominator 100.
• **Conversion is bidirectional**: To convert a fraction to percentage, multiply by 100. To convert percentage to fraction, divide by 100 and simplify.
• **Percentage of a quantity**: To find x% of N, compute (x/100) × N. This is the most common calculation in every problem.
• **Percentage increase/decrease**: If a value changes from A to B, percentage change = [(B − A)/A] × 100. Positive means increase, negative means decrease.
• **Successive percentage changes do not add**: If a value increases by 10% then decreases by 10%, the net effect is NOT zero. Use the formula: Net% = a + b + (ab/100) where a and b are the two percentage changes.
• **Percentage point vs percentage change**: If an exam pass rate rises from 40% to 50%, the percentage point increase is 10, but the percentage increase is (10/40) × 100 = 25%.
• **Reverse percentage**: If the final value after x% increase is known, the original value = Final/(1 + x/100). For decrease, use Final/(1 − x/100).
• **Common fraction–percentage pairs speed up calculation**: Memorize 1/2 = 50%, 1/3 = 33⅓%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16⅔%, 1/8 = 12.5%, 1/10 = 10%, 3/4 = 75%, 2/5 = 40%, 3/5 = 60%.

Formulas / Key Facts

1. **Basic percentage**: x% = x/100 2. **Percentage of N**: x% of N = (x/100) × N 3. **Percentage change**: [(New Value − Old Value)/Old Value] × 100 4. **Percentage increase**: New Value = Old Value × (1 + increase%/100) 5. **Percentage decrease**: New Value = Old Value × (1 − decrease%/100) 6. **Successive changes**: Net% = a + b + (ab/100) for changes a% and b% 7. **Three successive changes**: Net% = a + b + c + (ab + bc + ca)/100 + abc/10000 8. **Reverse calculation after increase**: Original = Final/(1 + x/100) 9. **Reverse calculation after decrease**: Original = Final/(1 − x/100) 10. **Fraction to percentage**: Multiply by 100 and add % symbol 11. **Percentage to decimal**: Divide by 100 12. **If A is x% more than B**: A = B(1 + x/100), so B = A/(1 + x/100) = A × 100/(100 + x) 13. **If A is x% less than B**: A = B(1 − x/100), so B = A/(1 − x/100) = A × 100/(100 − x)