Successive Percentage Change
Combine two percentage changes into one in a single step.
\text{Net change} = a + b + \dfrac{ab}{100}\,\%
1How it works
Instead of applying two percentage changes one after another, this formula gives the single net change in one go. Use a minus sign for a decrease.
2How to apply (in seconds)
- Write the two changes as a and b (negative for a decrease).
- Compute a + b + (a×b)/100.
- A positive result is a net increase; a negative result is a net decrease.
3Worked examples
Example 1 Worked solution
Q. A price is increased by 20% then decreased by 10%. Net change?
- a = +20, b = −10.
- Net = 20 + (−10) + (20 × −10)/100.
- = 10 − 2.
✓ +8% (net increase)
Example 2 Worked solution
Q. Two successive discounts of 20% and 25%. Single equivalent discount?
- a = −20, b = −25.
- Net = −20 − 25 + (−20 × −25)/100.
- = −45 + 5.
✓ 40% discount
4When to use it
- ✦Successive discounts and successive hikes.
- ✦Population growth or decline over two periods.
5Cautions & tips
- !Always make a decrease negative.
- !Order does not matter — a and b can be swapped.