Important Formulas & Concepts

Percentage

Quantitative Aptitude Study Mode

Percentage

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Important Formulas & Concepts

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Percentage

Percentage is one of the most important and highest-scoring topics in Quantitative Aptitude. Questions from this chapter are frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement examinations.

Most arithmetic chapters such as Profit & Loss, Simple Interest, Compound Interest, Average, Ratio & Proportion, Data Interpretation, and Mensuration directly or indirectly use percentage concepts.

Percentage-based questions generally involve:

  • Percentage increase and decrease
  • Successive percentage changes
  • Profit and loss percentages
  • Population growth
  • Depreciation
  • Discount and rebate
  • Error percentages
  • Comparison of quantities

Why Percentage is Important?

  • Foundation topic for many arithmetic chapters.
  • Frequently asked in competitive examinations.
  • Useful in daily life calculations.
  • Improves calculation speed and accuracy.
  • Essential for Data Interpretation and business mathematics.

What is Percentage?

The term percent means:

Per Hundred

Percentage is represented using the symbol:

%

A percentage can be defined as:

A fraction whose denominator is 100.

Basic Percentage Formula

If x percent is written mathematically:

x% = x / 100

Example:

20% = 20/100

= 1/5

Conversion Between Percentage, Fraction, and Decimal

Percentage Fraction Decimal
50% 1/2 0.5
25% 1/4 0.25
20% 1/5 0.2
10% 1/10 0.1
75% 3/4 0.75
12.5% 1/8 0.125
33.33% 1/3 0.333
66.66% 2/3 0.666

Converting Fraction into Percentage

To convert a fraction into percentage:

(Fraction × 100)%

Example:

1/4 × 100

= 25%

Converting Percentage into Fraction

To convert percentage into fraction:

x% = x/100

Example:

40%

= 40/100

= 2/5

Percentage Increase Formula

If a quantity increases from Old Value to New Value:

Percentage Increase = [(New − Old)/Old] × 100

Example:

Price increases from 500 to 600.

Increase:

= 600 − 500

= 100

Percentage increase:

= (100/500) × 100

= 20%

Percentage Decrease Formula

If a quantity decreases from Old Value to New Value:

Percentage Decrease = [(Old − New)/Old] × 100

Example:

Value decreases from 800 to 680.

Decrease:

= 800 − 680

= 120

Percentage decrease:

= (120/800) × 100

= 15%

Successive Percentage Change

If a quantity changes successively by a% and b%:

Net Change = a + b + (ab/100)

Use positive sign for increase and negative sign for decrease.

Example:

Increase by 20% and then by 10%.

Net increase:

= 20 + 10 + (20 × 10)/100

= 32%

Population Growth Formula

If population increases by R% annually:

Population after n years = P(1 + R/100)n

Where:

  • P = Present population
  • R = Rate of increase
  • n = Number of years

Depreciation Formula

If value decreases by R% annually:

Value after n years = P(1 − R/100)n

Where:

  • P = Present value
  • R = Rate of depreciation
  • n = Number of years

Percentage Change in Consumption

1. Price Increase

If price increases by R%, reduction in consumption to maintain same expenditure:

[R / (100 + R)] × 100%

2. Price Decrease

If price decreases by R%, increase in consumption to maintain same expenditure:

[R / (100 − R)] × 100%

Important Percentage Relations

1. If A is R% More Than B

B is less than A by [R/(100 + R)] × 100%

2. If A is R% Less Than B

B is more than A by [R/(100 − R)] × 100%

Percentage Error Formula

Percentage error is calculated using:

[(Wrong Value − Correct Value)/Correct Value] × 100

Important Percentage Values to Remember

Fraction Percentage
1/2 50%
1/3 33.33%
2/3 66.66%
1/4 25%
3/4 75%
1/5 20%
1/8 12.5%
1/10 10%

Common Percentage Applications

  • Profit and Loss
  • Simple Interest
  • Compound Interest
  • Population Growth
  • Data Interpretation
  • Discount and Rebate
  • Tax Calculations
  • Examination Marks

Important Formula Summary

Concept Formula
Percentage (Value/Total) × 100
Percentage Increase [(New − Old)/Old] × 100
Percentage Decrease [(Old − New)/Old] × 100
Successive Change a + b + ab/100
Population Growth P(1 + R/100)n
Depreciation P(1 − R/100)n

Common Mistakes in Percentage

  • Using wrong base value in percentage calculations.
  • Confusing percentage increase and decrease formulas.
  • Ignoring successive percentage effects.
  • Incorrect fraction-to-percentage conversion.
  • Calculation mistakes in decimal conversion.

Important Exam Tips

  • Memorize common percentage-fraction conversions.
  • Always identify the base value carefully.
  • Use decimal multiplication for faster calculations.
  • Practice successive percentage changes regularly.
  • Learn percentage shortcuts for quick mental calculation.
  • Use approximation techniques in objective questions.
  • Practice population and depreciation formula applications.

Percentage is one of the most fundamental and scoring chapters in Quantitative Aptitude. Strong understanding of percentage concepts, formulas, and applications helps candidates solve arithmetic and data interpretation questions quickly and accurately in competitive examinations.

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