Three Types of Percentage Problems — Solved
Percentage calculations come up constantly in everyday life — sales discounts, test scores, salary raises, tax rates, nutritional labels, investment returns, and more. Despite this, many people find percentage maths confusing. There are really only three core types of percentage problems, and once you understand each one, you can handle any percentage situation.
Type 1: Finding a Percentage of a Number
"What is X% of Y?" Formula: Answer = (X ÷ 100) × Y
Examples: What is 20% of $85? = 0.20 × 85 = $17.00. What is 7.5% tax on a $200 item? = 0.075 × 200 = $15.00. What is 35% of 180 (e.g. exam score)? = 0.35 × 180 = 63 marks.
Type 2: Percentage Change (Increase or Decrease)
"What is the % change from A to B?" Formula: ((B − A) ÷ |A|) × 100
Examples: Price rises from $80 to $96: ((96−80)÷80)×100 = +20% increase. Your weight goes from 85 kg to 79 kg: ((79−85)÷85)×100 = −7.1% decrease. Stock falls from $150 to $120: ((120−150)÷150)×100 = −20% drop.
| Situation | Original | New | Change |
|---|---|---|---|
| Salary raise | $55,000 | $60,000 | +9.1% |
| Price reduction | $299 | $249 | −16.7% |
| Population growth | 1,200,000 | 1,380,000 | +15.0% |
| Website traffic drop | 45,000 | 38,000 | −15.6% |
Type 3: Reverse Percentage (Finding the Original Value)
"Y is X% of what number?" Formula: Original = Y ÷ (X ÷ 100)
Examples: A discounted item costs $75 after 25% off — what was the original price? Original = 75 ÷ 0.75 = $100. An employee earned $4,500 after a 10% bonus — what was the base salary? 4,500 ÷ 1.10 = $4,090.91. A student got 72 marks, which was 60% of the total — total marks = 72 ÷ 0.60 = 120.
Common Percentage Mistakes to Avoid
Mistake 1 — Percentage increase then decrease is not zero. A price rises 20% then drops 20%. Is it back to original? No. $100 → +20% = $120 → −20% = $96. You are left with less than you started.
Mistake 2 — Confusing percentage points with percentages. If an interest rate rises from 2% to 3%, that is a 1 percentage point increase — but a 50% increase in the rate itself. Journalists and politicians often blur this distinction.
Mistake 3 — Using the wrong base. Is a 10% discount calculated on the original price or the sale price? Always clarify. "10% off $100" = $90. But "the sale price is 10% less than something" could be different if the percentage is on the final, not original price.
Percentages in Financial Life
Interest rates: A 5% APR on a $10,000 loan costs $500/year in interest. A 1% difference on a $300,000 mortgage = $3,000/year.
Salary negotiations: A 3% raise on $50,000 = $1,500/year. A 10% raise = $5,000/year. The percentage seems small; the dollar amount often surprises.
Investment returns: The S&P 500 averages ~10% annual return. At that rate (Rule of 72), money doubles every 7.2 years. A 2% fee on a fund seems tiny but reduces a $100k investment's 30-year growth by over $100,000 due to lost compounding.
Frequently Asked Questions
How do I calculate percentage in my head quickly?
For 10%: move the decimal point one place left ($85 → $8.50). For 5%: halve the 10% amount ($8.50 → $4.25). For 20%: double the 10% amount ($8.50 → $17.00). For 15%: add 10% + 5% ($8.50 + $4.25 = $12.75). Build up any percentage from these anchors.
What is the percentage formula I can use in Excel or Google Sheets?
Percentage of a number: =A1*B1/100. Percentage change: =(B1-A1)/ABS(A1)*100. Reverse percentage: =A1/(B1/100). Format the cell as a percentage to avoid manual multiplication by 100.
What does "basis point" mean?
A basis point (bp or bps) is one hundredth of a percentage point — i.e., 0.01%. It is used in finance to describe small changes in interest rates, fees, and yields. 25 basis points = 0.25%. 100 basis points = 1%.
How do I calculate a percentage increase for a raise request?
Divide your desired new salary by your current salary and subtract 1: ($65,000 ÷ $55,000) − 1 = 0.182 = 18.2% increase. Present both the dollar amount and the percentage — the percentage frames the ask relative to your value.
Can a percentage be more than 100%?
Yes. If something triples in value, that is a 200% increase (the new value is 300% of the original). Sales that grew from $50,000 to $175,000 increased by 250%. Percentages above 100% simply mean the change exceeds the original value.
How do I calculate a tip percentage quickly?
Double the tax (works in ~8–10% tax states to get ~16–20% tip). Or: move the decimal on the bill for 10%, then scale up. $64 bill: 10% = $6.40, 20% = $12.80, 15% = $9.60. Use our tip calculator to do this instantly.