Percentage Formulas: 5 Core Concepts with Worked Examples

Placement aptitude papers (TCS NQT, campus drives for data-analytics roles) consistently carry 4 to 6 direct percentage questions per test; a percentage is parts per hundred, and every question reduces to one of five formulas.

This article covers the complete set of formulas, with six worked examples verified from first principles, and a table of fraction equivalents for speed arithmetic. If you’re also working through time and work problems, the ratio logic there is the same root concept.

What Is a Percentage?

The word “percent” comes from the Latin per centum, meaning “by the hundred.” According to Khan Academy’s introduction to percentages, a percentage is simply a ratio with 100 as the denominator, and every percentage problem can be restated as a fraction or decimal.

Conversion rules:

• Fraction to percent: multiply by 100. Example: 3/4 = (3/4) × 100 = 75%
• Decimal to percent: move decimal two places right. Example: 0.375 = 37.5%
• Percent to fraction: divide by 100. Example: 45% = 45/100 = 9/20
• Percent to decimal: move decimal two places left. Example: 12.5% = 0.125

The base formula:

Percentage Value = (Part / Whole) × 100

• Example: 18 out of 60 students passed. Pass percentage = (18/60) × 100 = 30%.

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5 Core Percentage Formulas

Formula 1: Percentage of a Number

Find what X% of a given quantity is.

• Result = (X/100) × Quantity
• Example: 35% of ₹4,000 = (35/100) × 4,000 = ₹1,400

Formula 2: Percentage Change (Increase or Decrease)

Measures how much a value changed relative to its starting point.

• % Change = ((New Value - Original Value) / Original Value) × 100
• Positive result = increase; negative result = decrease.

Formula 3: Multiplication Factor

Shortcut to compute the new value in one step:

• For an increase of i%: Multiplication Factor = 1 + i/100
• For a decrease of d%: Multiplication Factor = 1 - d/100
• New Value = Original Value × Multiplication Factor

This avoids computing the absolute change separately and chains cleanly for successive changes.

Formula 4: Successive Percentage Change

When two (or more) percentage changes apply one after another:

• Net change = p + q + (p × q) / 100

Where p and q are the first and second percentage changes (use negative values for decreases).

The multiplication-factor version: Effective Factor = (1 + p/100) × (1 + q/100)

Both forms give the same answer; the formula version is faster for mental arithmetic.

Formula 5: Reverse Calculation (Find Original Value)

Given the final value and the percentage change, work back to the original.

• Original Value = Final Value / (1 + p/100)

For a percentage decrease: Original Value = Final Value / (1 - d/100)

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6 Worked Real-World Examples

Each example below is solved step by step. All arithmetic is independently verified.

Example 1: Salary Hike

• Given: Monthly salary ₹28,000; employer offers a 15% hike.
• Find: New salary.
• Step 1: Multiplication factor = 1 + 15/100 = 1.15
• Step 2: New salary = 28,000 × 1.15 = ₹32,200
• Answer: ₹32,200 per month.

Example 2: Exam Score as Percentage

• Given: Scored 54 marks out of 90.
• Find: Percentage score.
• Step 1: % = (54/90) × 100
• Step 2: 54/90 = 0.6; 0.6 × 100 = 60%
• Answer: 60%.

Example 3: Profit Percentage (P&L)

• Given: Bought an item at ₹250, sold at ₹300.
• Find: Profit percentage.
• Step 1: Profit = 300 - 250 = ₹50
• Step 2: % Profit = (50/250) × 100 = 20%
• Answer: 20% profit on cost price.

Example 4: Successive Price Change

• Given: A product price rises 20% in January, then falls 10% in March.
• Find: Net percentage change.
• Method A (multiplication factors): 1.20 × 0.90 = 1.08, so net +8%
• Method B (formula): p = 20, q = -10, so 20 + (-10) + (20 × -10)/100 = 10 - 2 = +8%
• Answer: Net increase of 8%, not 10%. The two changes do not simply add.

Example 5: Election Votes

• Given: 8,000 eligible voters; candidate A wins 55% of votes cast.
• Find: Votes received by A.
• Step 1: Votes = (55/100) × 8,000 = 4,400
• Answer: Candidate A receives 4,400 votes.

Example 6: Reverse — Find the Original Price

• Given: After a 25% increase, a product costs ₹75,000.
• Find: Original price before the hike.
• Step 1: Original = 75,000 / (1 + 25/100) = 75,000 / 1.25 = ₹60,000
• Answer: ₹60,000.

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Speed Tricks for Aptitude Tests

The 10% Method

Drop the last digit of the number to get one-tenth of it, then scale up or down to any multiple of five:

• 10% of 420 = 42
• 35% of 420 = (3 × 42) + (0.5 × 42) = 126 + 21 = 147
• 15% of 240 = 24 + 12 = 36

Fraction Equivalents Table

Memorising these cuts mental-arithmetic time on standard aptitude tests:

Fraction	Percentage
1/2	50%
1/3	33.33%
2/3	66.67%
1/4	25%
3/4	75%
1/5	20%
2/5	40%
3/5	60%
4/5	80%
1/6	16.67%
1/7	14.29%
1/8	12.5%
1/9	11.11%
1/10	10%
1/12	8.33%

Successive Change Quick Check

Apply the formula p + q + pq/100 mentally instead of long multiplication:

• Two rises of 10%: net = 10 + 10 + (10 × 10)/100 = 10 + 10 + 1 = 21%
• Rise of 10% then drop of 10%: net = 10 + (-10) + (10 × -10)/100 = 0 - 1 = -1% (you lose 1%)
• Rise of 20% then drop of 20%: net = 20 + (-20) + (20 × -20)/100 = 0 - 4 = -4%

Percentage Points vs. Percentage Change

A common source of errors in DI questions:

• If a pass rate rises from 40% to 55%, the rise is 15 percentage points.
• Expressed as a percentage change: (15/40) × 100 = 37.5% increase.
• Examiners use both framings; read the question carefully to know which is being asked.

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Percentages in Placement Tests

Percentage arithmetic appears in every major campus placement paper. The ZS Associates aptitude test uses data interpretation sets where DI tables require computing percentage share and growth. The Mu Sigma aptitude test (MuApT) is heavy on ratio and percentage questions embedded in case-let DI blocks, exactly the format where the successive-change formula saves time.

In both formats, the fastest candidates don’t recalculate from scratch. They match the fraction table in this article to the given number and build from there.

The same underlying logic (comparing one number to a baseline, tracking cumulative change) is what AI engineers use when reading model evaluation dashboards. A model accuracy going from 68% to 74% to 79% across three training runs is a successive percentage increase problem. TinkerLLM at ₹299 is where that transition starts: short LLM experiments where the output you’re interpreting is probability distributions and confidence scores, not abstract statistics.