Percentages · level 2
Discounts and mark-ups
Never compute the part and then subtract if you can help it. A 15% discount leaves 85% — one multiplication by 0.85 finishes the job, and the same trick handles tax, tips and interest.
Worked example: 240 − 15%
start240
15% part36
multiplier0.85
after the cut204
Step by step
- 1
Find the 15% part
15% of 240 = 36
Use the 10% and 1% blocks.
- 2
Take it off
240 − 36 = 204
- 3
Or do it in one move with a multiplier
240 × 0.85 = 204
A 15% cut leaves 85% of the original.
240 − 15% = 204
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.