Percentages · level 2
Working the percentage out
Going backwards is one division, not a formula. Work out 1% of the whole, then see how many of those the part contains — that count is the percentage.
Worked example: 12 is what % of 80?
part12
whole80
1% of whole0.8
answer15%
Step by step
- 1
Write it as a fraction of the whole
12 / 80
- 2
Compare with 1% of the whole
1% of 80 = 0.8
How many of those fit into the part?
- 3
Divide
12 ÷ 0.8 = 15%
12 is what % of 80? = 15
The theory behind it
Intuition
Any percentage is built from 10% and 1% blocks: 17% = 10% + 5% + 2%. Because x% of y equals y% of x, you can always take the easier direction.
Common pitfalls
- ×Adding percentage points to percentage changes — a rise from 4% to 6% margin is +2pp, not +2%.
- ×Reversing a discount by adding the same percentage back: −20% then +20% does not return to par.
In the interview
Margin, growth, share and discount questions — the single most common arithmetic in an interview.