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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.

percentage change = (change ÷ original value) × 100

Method 1: find the change first

Example: A monthly fee rises from ₹1,250 to ₹1,475.
  1. Find the increase: 1475 − 1250 = 225.
  2. Compare the increase with the original: 225 ÷ 1250 = 0.18.
  3. 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.

Example: Increase ₹2,400 by 7.5%.
2400 × 1.075 = 2580

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. 0.12 gives only the increase amount; 1.12 gives the new total.

A ten-second sense check

Estimate before calculating. A 10% increase on ₹1,250 is about ₹125. So an 18% increase should be a little under ₹250. That makes ₹225 believable.

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.

Try one yourself

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.