Percentages come up constantly — discounts, tax, exam scores, commissions, profit margins. The maths is simple once you recognise which of the three standard percentage problems you're facing.
The Three Common Percentage Problems
Problem 1: What is X% of a number?
Formula: Result = Number × (Percentage ÷ 100)
Examples:
- 15% of 2,000 = 2,000 × 0.15 = 300
- 8% GST on a Rs 5,000 bill = 5,000 × 0.08 = Rs 400
- 30% discount on Rs 3,500 = 3,500 × 0.30 = Rs 1,050 off
Problem 2: What percentage is A of B?
Formula: Percentage = (A ÷ B) × 100
Examples:
- 45 correct out of 75 = (45 ÷ 75) × 100 = 60%
- You spent Rs 1,200 out of a Rs 5,000 budget = (1,200 ÷ 5,000) × 100 = 24%
- 18 out of 60 items sold = (18 ÷ 60) × 100 = 30%
Problem 3: X is Y% of what number?
Formula: Original = X ÷ (Y ÷ 100) or X ÷ Y × 100
Examples:
- 75 is 25% of what? = 75 ÷ 0.25 = 300
- Rs 240 is 12% of what total? = 240 ÷ 0.12 = Rs 2,000
Quick Mental Shortcuts
| % | Shortcut |
|---|---|
| 50% | Divide by 2 |
| 25% | Divide by 4 |
| 10% | Divide by 10 (move decimal one left) |
| 5% | Find 10%, then halve it |
| 1% | Divide by 100 |
| 20% | Find 10%, then double it |
For any of these: find 10% first (divide by 10), then build from there. 15% = 10% + 5%.
Percentage Calculator
For any combination of values, the Percentage Calculator handles all three problem types. For percentage changes (increase or decrease), that's a related but slightly different calculation — see how to calculate percentage increase and decrease.
Real-World Applications
In Pakistan's business context, percentages come up constantly: FBR's income tax slabs use percentages, bank profit rates are quoted as percentages, e-commerce commission rates are percentages of sale price, and salary increments are percentage increases. For any of these calculations involving time (e.g. monthly vs annual rates), make sure you're using the same time basis throughout. A 12% annual profit rate divided by 12 gives 1% per month — mixing these without conversion produces wrong results.
Percentage vs Absolute Numbers
A percentage always needs context to be meaningful. "20% more sales" is excellent if last month had 100 sales (20 more); it's less significant if it was 1 sale to 1.2. Always present both the percentage and the absolute number when communicating results. Use Percentage Calculator for any calculation, and how to calculate percentage increase and decrease for change over time.
