The three most common percentage problems, all solved instantly with no algebra required.
Four panels, four questions, and they are not interchangeable. The first answers "what is X% of Y". The second answers "X is what percent of Y". The third gives the change from one number to another. The fourth adds or removes a percentage from a starting number. Putting a number in the wrong panel is the most common way to get a confident wrong answer.
Pick by what you already know. If you know the percentage and the total and want the part, use panel one. If you know the two numbers and want the percentage, use panel two or three.
With the defaults on the page:
| Question | Answer |
|---|---|
| 15% of 200 | 30 |
| 30 is what percent of 200 | 15.00% |
| Change from 80 to 100 | +25.00% |
| 100 plus 20% | 120.00 |
| 100 minus 20% | 80.00 |
Now the trap in one line: 100 up 20% is 120, and 120 down 20% is 96. You are four short of where you started, because the second 20% was taken from a bigger base. A pay cut of 20% followed by a raise of 20% leaves you worse off, and no amount of repeating the sequence gets you back.
Percentage change is always measured against the starting value, which is why a move from 80 to 100 is a 25% increase and a move from 100 to 80 is a 20% decrease. Same 20 points, two different percentages, both correct. When a figure "rose 5%" and the next report says it "fell 5%", the level is now lower than it was two reports ago.
Percentage points are not percentages. A fee going from 10% to 12% has risen by 2 percentage points and by 20% of itself. Lenders and news reports mix the two constantly, and the difference between them is usually the whole story.
The mental arithmetic worth learning is the tens trick. Ten percent is the decimal point moved one place left. Fifteen percent is that plus half of it. Twenty percent is twice it. A 15% tip on $64 is $6.40 plus $3.20, so $9.60. That covers most of the percentages anyone meets at a counter.
Because the increase of 20 is measured against the starting value of 80. Twenty divided by eighty is 25%.
Take 10%, then add half of that for the remaining 5%. On $60, 10% is $6 and 5% is $3, so 15% is $9.
Going from 10% to 12% is 2 percentage points, but a 20% increase in the rate itself. Both statements describe the same move.
No. $100 down 20% is $80, and $80 up 20% is $96. The second change is based on the smaller number.
Divide by one minus the discount. A price of $72 after 20% off means the original was 72 ÷ 0.8, which is $90.
Percent change is ordinary arithmetic. There is no agency that defines it differently.
Last updated: November 2, 2026. Reviewed by David Liu.