Percentage Increase and Decrease: Choosing the Right Method
Learn percentage increase and decrease with the change method, multiplier method, worked examples, checks and common mistakes.
The core idea
A percentage change compares the change with the original value. That last word matters. If a price moves from ₹800 to ₹920, the change is ₹120, but the percentage increase is not 120 ÷ 920. You divide by the starting value, ₹800.
Method 1: find the change first
- Find the increase:
1475 − 1250 = 225. - Compare the increase with the original:
225 ÷ 1250 = 0.18. - Convert to a percentage:
0.18 × 100 = 18%.
Answer: 18% increase.
The same method works for a decrease. If a value falls, find original − new to keep the size of the decrease positive.
Method 2: use a multiplier
For repeated calculations, multipliers are faster. A 12% increase means keep 100% and add 12%, so multiply by 1.12. A 12% decrease means keep 88%, so multiply by 0.88.
New value: ₹2,580.
Why the multiplier works
Because 100% of a quantity is the whole quantity. So 107.5% is 107.5 ÷ 100 = 1.075 times the original. The multiplier is just the percentage written as a decimal scale factor.
Where percentage-change answers usually go wrong
- Dividing by the new value. Percentage change normally uses the original value as the reference.
- Subtracting 12 from a number for a 12% decrease. Percent means “per hundred”, not a fixed amount.
- Using 0.12 instead of 1.12 for an increase.
0.12gives only the increase amount;1.12gives the new total.
A ten-second sense check
If the question asks for the new amount, use a multiplier. If it asks for the percentage change between two values, use change ÷ original × 100.
A value rises from 500 to 575. What is the percentage increase?
Keep going
For another problem using related ideas, return to the Fractions, Ratios & Percentages page.