Increases, discounts and percentages in everyday life

Increasing a number by a percentage

To increase an initial price P by p%, calculate:

new price = P × (1 + p/100)

Example: an item costs 80 euros; its price increases by 15 per cent.

new price = 80 × (1 + 15/100) = 80 × 1.15 = 92 euros.

Reducing a number by a percentage (discount, sale)

To reduce an initial price P by p%, calculate:

new price = P × (1 – p/100)

Example: an item costing 80 euros is on offer with a 30 per cent discount.

new price = 80 × (1 – 30/100) = 80 × 0.7 = 56 euros.

First pitfall: discounts do not add up

Two successive discounts of 10% do not add up to a total discount of 20%! On 100 euros: -10% gives 90 euros, then -10% on 90 euros gives 81 euros. The total discount is therefore 19 per cent, not 20 per cent.

Second pitfall: increasing and then decreasing by the same percentage does not return you to the original price

If you increase 100 euros by 20 per cent, you get 120 euros. If you then reduce those 120 euros by 20 per cent, you get 120 × 0.8 = 96 euros, not 100 euros! The percentage is applied to a different value at each stage, so you must always recalculate based on the new price.