Numerical aptitude · Percentages and money
Percentages, made easy
💡 The idea
Per cent just means “out of 100”. 20% means 20 out of every 100.
🧭 The method: 3 steps
- Turn the per cent into a fraction: 20% = 20/100.
- Multiply it by the number you are taking it of.
- For a change (up or down), always compare with the starting number.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
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✏️ Worked examples
Example 1. What is 20% of 150?
- 20% = 20/100
- 20/100 × 150 = 3000/100
- = 30
⚡ Shortcut: 10% of 150 is 15 (move the decimal one place). 20% is double: 30.
Example 2. A price goes from $80 to $100. What is the percentage increase?
- Change = 100 − 80 = 20
- Compare with where it started: 20 ÷ 80 = 0.25
- 0.25 × 100 = 25%
⚡ Shortcut: Change ÷ old × 100.
Example 3. After a 25% rise a salary is $500. What was it before?
- Old salary = 100%. New = 125%.
- 125% is $500, so 1% is 500 ÷ 125 = 4
- 100% = 4 × 100 = $400
⚡ Shortcut: 500 ÷ 1.25 = 400.
⚠️ Where people go wrong
- Taking 25% off $500 does not give the old salary ($375 is wrong): the 25% was of the old salary.
- Up 10% and then down 10% is not back to the start: 100 → 110 → 99, a 1% fall.
- For “% increase”, divide by the old number, never the new one.
📌 Remember
- x% of N = x/100 × N
- % change = change ÷ old × 100
- 10% = move the decimal one place left