Key points
- X% of Y = Y × X ÷ 100.
- Percentage change = (new − old) ÷ old × 100 — a rise from 80 to 100 is 25%, a fall from 100 to 80 is 20%.
- “30% off + 10% extra” is a 37% discount, not 40%.
- A 25% markup is only a 20% profit margin.
The core formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 18% of ₹2,500 = ₹450 |
| X is what % of Y? | X ÷ Y × 100 | ₹450 of ₹2,500 = 18% |
| Percentage increase | (New − Old) ÷ Old × 100 | ₹80 to ₹100 = +25% |
| Percentage decrease | (Old − New) ÷ Old × 100 | ₹100 to ₹80 = −20% |
| Value after a % increase | Value × (1 + % ÷ 100) | ₹50,000 + 8% = ₹54,000 |
| Original before a % increase | Final ÷ (1 + % ÷ 100) | ₹54,000 ÷ 1.08 = ₹50,000 |
Why up and down are not symmetrical
A share that falls 50% needs to rise 100% to get back where it started. A salary cut of 20% needs a 25% raise to be undone. Percentage changes are always measured against the starting value, and the starting value is different on the way back.
Stacked discounts
Successive discounts multiply rather than add. “30% off, plus an extra 10%” on ₹1,000: first ₹1,000 × 0.70 = ₹700, then ₹700 × 0.90 = ₹630. The total discount is 37%, not 40%. The discount calculator handles stacked offers and GST on the discounted price.
Markup vs margin
Markup is profit as a percentage of cost; margin is profit as a percentage of the selling price. An item that costs ₹100 and sells for ₹125 has a 25% markup but a 20% margin (₹25 ÷ ₹125). To hit a target margin, divide cost by (1 − margin): for a 30% margin on ₹100 cost, price = 100 ÷ 0.70 ≈ ₹142.86.
Percentage vs percentage points
When a loan rate rises from 8% to 9%, it rises by one percentage point — but by 12.5% in relative terms. News about interest rates, tax rates and inflation usually speaks in percentage points; be clear which one a figure means.
Quick mental shortcuts
- 10% of a number: move the decimal one place left. 10% of ₹4,500 is ₹450.
- 5% is half of 10%; 20% is double; 15% is 10% plus 5%.
- 1% of a number: move the decimal two places left, then multiply for any whole percentage.
- X% of Y equals Y% of X: 8% of 50 is the same as 50% of 8, which is 4.
Successive percentage changes
Percentages applied one after another multiply. A price that rises 10% and then falls 10% ends 1% lower (1.10 × 0.90 = 0.99). Three years of 10% growth add up to 33.1%, not 30% (1.1³ = 1.331). This is compounding at work — the same reason salaries, investments and prices grow faster over time than simple addition suggests.
To find the overall change from several steps, multiply the factors (1 + each change) and subtract 1. For a 5% salary cut followed by a 12% raise: 0.95 × 1.12 = 1.064, an overall rise of 6.4%.
Frequently asked questions
How do I calculate a percentage of a total in Excel?
Use =Part/Total and format the cell as a percentage, or =Part/Total*100 for a plain number.
How do I calculate marks percentage?
Divide the marks obtained by the maximum marks and multiply by 100. 432 out of 500 is 432 ÷ 500 × 100 = 86.4%.
What is the formula for percentage increase?
(New value − Old value) ÷ Old value × 100. A salary rising from ₹60,000 to ₹66,000 is a 10% increase.